If the nth term is nn+1, then the (n+1)st term is:

Answer:

The critical value for two tailed test at alpha=0.1 is ± 1.645

The calculated  z= 9.406

Step-by-step explanation:

Formulate the hypotheses as

H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods

Ha : p1≠ p2

Choose the significance level ∝= 0.1

The critical value for two tailed test at alpha=0.1 is ± 1.645

The test statistic is

Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]

p1= scrap rate of old method = 62/200=0.31

p2= scrap rate of new method = 36/400= 0.09

p = an estimate of the common scrap rate on the assumption that the two rates are same.

p = n1p1+ n2p2/ n1 + n2

p =200 (0.31) + 400 (0.09) / 600

p= 62+ 36/600= 98/600 =0.1633

now q = 1-p= 1- 0.1633= 0.8367

Thus

z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)

z= 0.301/√ 0.13663( 3/400)

z= 0.301/0.0320

z= 9.406

The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.

Answer:

Cohen's D

Step-by-step explanation:

Cohen's D is a statistic that measures effect size. It shows standardised difference between 2 means.

Effect size is defined as how large the effect of a something is or its magnitude.

Cohen's D works effectively when the sample is >50 (that is for large samples). However a correction factor can be used to make results from small samples more accurate

The formular for Cohen's D is:

D = (mean1 - mean2) ÷ (√({standard deviation1}^2 + {standard deviation 2}^2)/2)

This is the most appropriate method in the given scenario

Answer:

option a

Step-by-step explanation:

give person above brainliest :)

Answer:

x = 38.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan x = 8/10

taking the inverse tan of each side

x = tan ^-1 (8/10)

x=38.65980825

To the nearest tenth

x = 38.7

Answer:

[tex] \frac{1}{3} [/tex]Rational number as denominator is not equal to zero and numerator is a integer.

Rational numbers. denoted by [tex] \mathbb Q[/tex]

1/3 is clearly not a natural number or integer.

it is a fraction, =0.333 , it fits the definition of rational number ([tex] \frac pq [/tex]).

Answer:

The third option.

Step-by-step explanation:

Mathematical induction is a 2 step mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.

Step 1 (Base step) - It proves that a statement is true for the initial value.

Step 2 (Inductive step) - It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n + 1)th iteration (or number n + 1)

Hope this helps.

Please mark Brainliest.

Answer:

A method of improving statments

Step-by-step explanation:

"Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number."

Answer:

(i) 0.32          (ii) 0.85

(iii) 0.3412    (iv) 0.20

(v) 0.29         (vi) 0.12

Step-by-step explanation:

The data provided is as follows:

   Race                    Smoker (S)         Nonsmoker (N)             Row Total

 White(W)                    290                       560                           850

  Black(B)                     30                        120                           150

Column Total                320                       680                        1,000

(i)

Compute the value of P (S) as follows:

[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]

P (S∩W) = 0.12.

Answer:

Step-by-step explanation:

From the given information;

Angela took a general aptitude test and scored in the 90th percentile for aptitude in accounting.

What percentage of the scores were at or below her score?

The percentage of scores that were at or below her score is

Percentage P = 90%

This benchmark is more than average, so we can typically say more of the scores were at or below her score

What percentage were above?

Since The percentage of scores that were at or below her score is

Percentage P = 90%

Then the percentage of the scores that were above will be : (100 -90)%

= 10 %

We can see here that  less percentage of score were above Angela's Score.

Answer:

see below

Step-by-step explanation:

the simple answer is -270000

Answer:

The speed of the airplane in still air is 550 mph.

The speed of the wind is 50 mph.

Step-by-step explanation:

speed = distance / time

distance = speed * time

or simply

d = st

Let v be the speed of the airplane with no wind.

Let w = speed of wind

With the wind:

d = 1800; s = v + w; t = 3

1800 = 3(v + w)

Against the wind:

d = 1800; s = v - w; t = 3.6

1800 = 3.6(v - w)

We have a system of two equations:

3(v + w) = 1800

3.6(v - w) = 1800

Divide both sides of the first equation by 3. Divide both sides of the second equation by 3.6.

v + w = 600

v - w = 500

Add the equations.

2v = 1100

v = 550

The speed of the airplane in still air is 550 mph.

v + w = 600

550 + w = 600

w = 50

The speed of the wind is 50 mph.

Answer:

(x=6) is less than 18 which would give you the cost of the current plan

Step-by-step explanation:

If you take six, first you must multiply 4.50 by 6, ($27) then add it, to $94, giving you $121. Now we have to find which phone will give us the same cost, for this I choose 18. if you do 18 x 4.50, you get $81, and if you add this to 94, it gives you 175.

Answer: 3

Step-by-step explanation:

first, we know that:

1 + 2 + 3 + 4 +5 +6 = 21

Now, which two numbers we should take out in order to have 15?

we can remove the 2 and the 4, or the 1 and the 5.

so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)

in the other arrange, we have that removing two numbers we should get 12.

in order to reach 12, we should remove two numbers that add 9 together.

those can be 4 and 5, or 6 and 3.

Now, notice that in the first restriction we have that:

Or 2 and 4 are opposite,

or 1 and 5 are opposite.

So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.

Then we can affirm that the value that appears in the face opposite to the 6, is the 3.

Answer:

219.80 feet

Step-by-step explanation:

Tan 20= 80/b

Tan 20= 0.363970234266

(0.363970234266)b=80

b= 219.80 feet

The distance between the sculpture and the bottom of the building is required.

The distance between the building and sculpture is 219.80 feet.

[tex]\theta[/tex] = Angle of depression = Angle of elevation = [tex]20^{\circ}[/tex]

p = Height of building = 80 feet

b = Required length

From the trigonometric ratios we have

[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow b=\dfrac{p}{\tan\theta}\\\Rightarrow b=\dfrac{80}{\tan 20}\\\Rightarrow b=219.80\ \text{feet}[/tex]

Learn more about trigonometry:

https://brainly.com/question/23899312

Answer:

0.90415

Step-by-step explanation:

Given the following :

Arrival rate = mean(μ) = 24

Probability that at most 30 customers arrive in the next hour:

The poisson distribution formula :

P(x, μ) = [(e^-μ) * (μ^x)] / x!

Where :

e = euler's constant

P(x ⩽ 30) = p(0) + p(1) + p(2) +.... + p(30)

Using the online poisson probability distribution calculator :

P(x ⩽ 30, 24) = 0.90415

Therefore there is about 90.4% probability that at most 30 customers will arrive in the next hour.

Answer:

The expression = [tex] \frac{40}{y - 16} [/tex]

Value of the expression = 4 (when y is 20)

Step-by-step explanation:

Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.

From the information given to us here,

the dividend = 40

the divisor = y - 16

The quotient = [tex] \frac{40}{y - 16} [/tex]

There, the expression would be [tex] \frac{40}{y - 16} [/tex]

Find the value of the expression when y = 20.

Plug in 20 for y in the expression and evaluate.

[tex] \frac{40}{y - 16} [/tex]

[tex] = \frac{40}{20 - 16} [/tex]

[tex] = \frac{40}{4} = 10 [/tex]

The value of the expression, when y is 20, is 4.

Answer:

32.8 miles

Step-by-step explanation:

Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?

Answer: The general equation of a line is given as y = mx + c, where m is the slope of the line and c is the intercept on the y axis. Given that the slope is -0.95, substituting in the general equation :

y = -0.95x + c

Amy has 48 miles remaining after 31 minutes of driving, to find c, we substitute y = 48 and x = 31. Therefore:

48 = -0.95(31) + c

c = 48 + 0.95(31)

c = 48 + 29.45

c = 77.45

The equation of the line is

y = -0.95x + 77.45

After 47 minutes of driving, the miles remaining can be gotten by substituting x = 47 and finding y.

y = -0.95(47) + 77.45

y = -44.65 + 77.45

y = 32.8 miles

Answer:

D question,somewhat confusing, itsit's like simultaneous equation,but values are different

Answer:

x = 4 + 2y/3

Step-by-step explanation:

Answer:

Yes it suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood.

Well if a significance level of 0.05 is used it will not affect the conclusion

Step-by-step explanation:

From the question we are told that

     The  sample size is   [tex]n = 149[/tex]

     The  number that where  type A blood is  k =  76

       The population proportion is   [tex]p = 0.40[/tex]

       The  significance level is  [tex]\alpha = 0.01[/tex]

Generally the sample proportion is mathematically represented as

      [tex]\r p = \frac{k}{n}[/tex]

=>    [tex]\r p = \frac{76}{149}[/tex]

=>    [tex]\r p = 0.51[/tex]

The  Null hypothesis is   [tex]H_o : p = 0.41[/tex]

The  Alternative hypothesis is  [tex]H_a : p \ne 0.40[/tex]

Next we obtain the critical value of [tex]\alpha[/tex] from the z-table.The value is  

       [tex]Z_{\alpha } = Z_{0.01} = 1.28[/tex]

Generally the test statistics is mathematically evaluated as

           [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1-p)}{n} } }[/tex]    

substituting values

           [tex]t = \frac{0.51 - 0.40 }{ \sqrt{ \frac{0.40 (1-0.40 )}{149} } }[/tex]    

           [tex]t =2.74[/tex]

So looking at the values for t  and  [tex]Z_{0.01}[/tex] we see that  [tex]t > Z_{0.01}[/tex] so we reject the null hypothesis. Which means that there is no sufficient evidence to support the claim

Now if [tex]\alpha = 0.05[/tex] , the from the z-table the critical value for [tex]\alpha = 0.05[/tex] is  [tex]Z_{0.05} = 1.645[/tex]

So comparing the value of  t and  [tex]Z_{0.05} = 1.645[/tex]  we see that [tex]t > Z_{0.05}[/tex] hence the conclusion would not be different.

Answer:

We conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

Step-by-step explanation:

We are given that the 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0.

Let [tex]\mu_1[/tex] = population mean score for children born to cocaine users.

[tex]\mu_2[/tex] = population mean score for children not exposed to cocaine.

So, Null Hypothesis, : = 490      {means that the prenatal cocaine exposure is not associated with lower scores of four-year-old children on the test of object assembly}

Alternate Hypothesis, : 490     {means that the prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                               T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~ [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean score of children born to cocaine users = 7.3

[tex]\bar X_2[/tex] = sample mean score of children not exposed to cocaine = 8.2

[tex]s_1[/tex] = sample standard deviation for children born to cocaine users = 3

[tex]s_2[/tex] = sample standard deviation for children not exposed to cocaine = 3

[tex]n_1[/tex] = sample of children born to cocaine users = 190

[tex]n_2[/tex] = sample of children not exposed to cocaine = 186

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(190-1)\times 3^{2}+(186-1)\times 3^{2} }{190+186-2} }[/tex] = 3

So, the test statistics =   ~

                                     =  -2.908

The value of t-test statistics is -2.908.

Now, at a 0.05 level of significance, the t table gives a critical value of -1.645 at 374 degrees of freedom for the left-tailed test.

Since the value of our test statistics is less than the critical value of t as -2.908 < -1.645, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

In the null hypothesis, a test always forecasts no effect, while the alternate theory states the research expectation impact, and calculation as follows:

Calculating the pooled estimator of [tex]\sigma^2[/tex], denoted by [tex]S^2_p[/tex], is defined by

[tex]\to \bold{S^2_p= \frac{(n_1 - 1) S^2_1+ (n_2 - 1)S^2_2}{n_1 + n_2 - 2}}[/tex]

Null hypothesis:

[tex]\to H_0 : \mu_1 - \mu_2 = \Delta_0\\[/tex]

Test statistic:

[tex]\to T_0=\frac{\bar{X_1}- \bar{X_2} -\Delta_0}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \\\\[/tex]

Alternative Hypothesis:

[tex]H_1 : \mu_1 -\mu_2 \neq \Delta_0\\\\ H_1 : \mu_1 -\mu_2 > \Delta_0\\\\H_1 : \mu_1 -\mu_2 < \Delta_0\\\\[/tex]

Rejection Criterion

[tex]t_0 > t_{\frac{\alpha}{2} , n_1+n_2 -2}\ \ \ or\ \ \ t_0 < - t_{\frac{\alpha}{2} , n_1+n_2 -2} \\\\t_o > t_{\alpha , n_1+n_2 -2} \\\\t_o > -t_{\alpha , n_1+n_2 -2}[/tex]

Given value:

[tex]\to S_p=9\\\\\to \Delta_0=0\\\\\to t_0=-\frac{0.9}{3(\sqrt{(\frac{1}{190}+\frac{1}{186})})}=-2.9\\\\\to t_{0.05,374}=1.645\\\\[/tex]

here

[tex]\to t_0 < -t_{0.05,374}[/tex]

hence rejecting the [tex]H_0[/tex]

Since there should be enough evidence that prenatal cocaine exposure is linked to inferior item assembly scores in 4-year-olds.

Find out more about the alternative hypothesis here:

brainly.com/question/18831983

Answer:

160 miles

Step-by-step explanation:

We can use a ratio to solve

220 miles         x miles

--------------- = ----------------------

5.5 hours          4 hours

Using cross products

220 *4 = 5.5x

880 = 5.5x

Divide each side by 5.5

880/5.5 = x

160 miles

Answer:

[tex]\large \boxed{\mathrm{C. \ 160 \ miles}}[/tex]

Step-by-step explanation:

We can solve this problem by ratios.

Let x be the missing value.

[tex]\displaystyle \frac{220}{5.5} =\frac{x}{4}[/tex]

Cross multiply.

[tex]5.5 \times x = 220 \times 4[/tex]

[tex]5.5x=880[/tex]

Divide both sides by 5.5.

[tex]\displaystyle \frac{5.5x}{5.5} =\frac{880}{5.5}[/tex]

[tex]x=160[/tex]

Answer:

10

Step-by-step explanation:

f(o) is given when x= 0 in f(x)

f(0) = 5 ( 0 + 2 ) 2 - 10

= 20 - 10

= 10

Answer:

[tex] \boxed{ \bold{ \huge{ \sf{f{(0) = 10}}}}}[/tex]

Step-by-step explanation:

Given, f ( x ) = 5 ( x + 2 )² - 10

Let's find f ( 0 ) :

[tex] \sf{f(0) = 5( {0 + 2)}^{2} - 10}[/tex]

Add the numbers

⇒[tex] \sf{f(0) = 5( {2)}^{2} - 10}[/tex]

Evaluate the power

⇒[tex] \sf{f(0) = 5 \times 4 - 10}[/tex]

Multiply the numbers

⇒[tex] \sf{ 20 - 10}[/tex]

Subtract 10 from 20

⇒[tex] \sf{10}[/tex]

Hope I helped !

Best regards !!

Answer:

rose. is. 18/2=9 years old

Answer:

Stephanie is 18years old and she is twice older than her sister

so rosa is 18÷2(since stephanie is twice older than rosa

so rosa is 9 years old

Answer:

[tex]f(x) =3\,*\,\,4^x[/tex]

Step-by-step explanation:

to find the equation of an exponential function, just points on the function's graph  are needed.

Recall that the exponential function has a general expression given by:

[tex]f(x) = a \,e^{b\,x}[/tex]

so we impose the condition for the function going through the first point (0,3) as:

[tex]f(0) = a \,e^{b\,(0)}= 3\\a\,e^0=3\\a\,(1)=3\\a = 3[/tex]

Now,knowing the parameter a, we can find the parameter b using the other point:

[tex]f(1) = 3 \,e^{b\,x}= 12\\3\,e^{b\,(1)}=12\\e^b=12/3\\e^b=4\\b=ln(4)[/tex]

Therefore, the function can be written as:

[tex]f(x) = 3 \,e^{ln(4)\,x}=3\,\,\,4^x[/tex]

Answer:

C)

h(x) = 3(4)x

Answer: -9/5

Step-by-step explanation: To find the slope, we must understand that the slope of a line is defined as the ratio rise/run.

The rise is the vertical direction of the line and the

run is the horizontal direction of the line.

So to start, I am going to pick 2 points on this line.

You want to find points where the line crosses the four corners.

In the diagram, those would be the points (-4, 5) and (1, -4).

Now, we can use slope formula.

Slope = y₂ - y₁ / x₂ - x₁

So we have -4 - 5/1 - -4 which simplifies to -9/5.

So the slope is -9/5.

Answer:

the answer is -9/5 100%

Step-by-step explanation:

Answer:

[tex] Perimeter = 3x + 3 [/tex]

Step-by-step explanation:

Perimeter of the given triangle in the figure is the sum of all three sides.

The expressions for the 3 sides are given as, [tex] x, (x - 3), (x + 6) [/tex].

Therefore,

[tex] Perimeter = x + (x - 3) + (x + 6) [/tex]

Simplify,

[tex] Perimeter = x + x - 3 + x + 6 [/tex]

Collect like terms

[tex] Perimeter = x + x + x - 3 + 6 [/tex]

[tex] Perimeter = 3x + 3 [/tex]

Answer:

34

Step-by-step explanation:

= 26 + 8

= 34

Answer:

La pendiente de la recta L es [tex]\frac{3}{2}[/tex].

Step-by-step explanation:

La recta está presentada en su forma implícita, es decir, que está bajo la forma:

[tex]f(x,y) = 0[/tex]

Para determinar la pendiente de la recta, se debe transformarla a su forma explícita, cuya fórmula es:

[tex]y = m \cdot x + b[/tex]

Donde:

[tex]x[/tex] - Variable independiente, adimensional.

[tex]y[/tex] - Variable dependiente, adimensional.

[tex]m[/tex] - Pendiente, adimensional.

[tex]b[/tex] - Intercepto, adimensional.

Entonces:

[tex]3\cdot x - 2\cdot y + 1 = 0[/tex]

[tex]2\cdot y = 3\cdot x +1[/tex]

[tex]y = \frac{3}{2}\cdot x + \frac{1}{2}[/tex]

Por simple inspección, se determina que la pendiente de la recta L es [tex]\frac{3}{2}[/tex].

Answer:

Step-by-step explanation:

from the question,

the mean 14

the standard deviation is 3

and sample size is 10.

since the n which is the sample size is 10, then the distribution is mound shaped.

why?

this is due to the fact that the random variable from which we took the sample is mound shaped.

The sampling distribution of the mean is normally distributed although the question says the random variable is not normally distributed. so the shape is bell shaped and normally distributed.

the standard deviation of the mean is

3/√10

= 0.948

Answer:

Explained below.

Step-by-step explanation:

Let X = systolic blood pressure measurements.

It is provided that, [tex]X\sim N(\mu=80,\sigma^{2}=3^{2})[/tex].

(a)

Compute the percentage of measurements that are between 71 and 89 as follows:

[tex]P(71<X<89)=P(\frac{71-80}{3}<\frac{X-\mu}{\sigma}<\frac{89-80}{3})[/tex]

                        [tex]=P(-3<Z<3)\\=P(Z<3)-P(Z<-3)\\=0.99865-0.00135\\=0.9973[/tex]

The percentage is, 0.9973 × 100 = 99.73%.

Thus, the percentage of measurements that are between 71 and 89 is 99.73%.

(b)

Compute the probability that a person's blood systolic pressure measures more than 89 as follows:

[tex]P(X>89)=P(\frac{X-\mu}{\sigma}>\frac{89-80}{3})[/tex]

                [tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]

Thus, the probability that a person's blood systolic pressure measures more than 89 is 0.0014.

(c)

Compute the probability that a person's blood systolic pressure being at most 75 as follows:

Apply continuity correction:

[tex]P(X\leq 75)=P(X<75-0.5)[/tex]

                [tex]=P(X<74.5)\\\\=P(\frac{X-\mu}{\sigma}<\frac{74.5-80}{3})\\\\=P(Z<-1.83)\\\\=0.03362\\\\\approx 0.034[/tex]

Thus, the probability that a person's blood systolic pressure being at most 75 is 0.034.

(d)

Let x be the blood pressure required.

Then,

P (X < x) = 0.15

⇒ P (Z < z) = 0.15

⇒ z = -1.04

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-1.04=\frac{x-80}{3}\\\\x=80-(1.04\times3)\\\\x=76.88\\\\x\approx 76.9[/tex]

Thus, the 15% of patients are expected to have a blood pressure below 76.9.

(e)

A z-score more than 2 or less than -2 are considered as unusual.

Compute the z score for [tex]\bar x[/tex] as follows:

[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]

  [tex]=\frac{84-80}{3/\sqrt{3}}\\\\=2.31[/tex]

The z-score for the mean blood pressure measurement of 3 patients is more than 2.

Thus, it would be unusual.

Answer:

  (3ab)/(2(b-a))

Step-by-step explanation:

The n-th term of an arithmetic progression is ...

  an = a1 +d(n -1)

Then the value of n is ...

  n = (an -a1)/d +1

The sum of an arithmetic progression is the product of the number of terms and the average of the first and last terms. In this sequence, the common difference d is ...

  d = (b -a)

So, the sum is ...

  Sn = (a +2a)/2·((2a -a)/(b -a) +1)

  Sn = (3ab)/(2(b-a)) . . . . sum of the arithmetic progression

__

Example:

The sequence 1, 1.5, 2 has ...

  a = 1, b = 1.5

Its sum is given by the above formula as ...

  Sn = 3(1)(1.5)/(2(1.5 -1)) = 4.5/(2(.5)) = 4.5 = 1 + 1.5 + 2 . . . . yes