Find the first four terms of the sequence given ai
31 and an+1
an
3.

Answers

Answer 1

Answer:

he arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence

Step-by-step explanation:

In an arithmetic sequence,

a_1=2a

1

=2

a_i=a_{i-1}-3a

i

=a

i−1

−3

To find:

The sum of the first 335 terms in the given sequence.

Solution:

The recursive formula of an arithmetic sequence is:

a_i=a_{i-1}+da

i

=a

i−1

+d ...(i)

Where, d is the common difference.

We have,

a_i=a_{i-1}-3a

i

=a

i−1

−3 ...(ii)

On comparing (i) and (ii), we get

d=-3d=−3

The sum of first i terms of an arithmetic sequence is:

S_i=\dfrac{i}{2}[2a+(i-1)d]S

i

=

2

i

[2a+(i−1)d]

Putting i=335,a=2,d=-3i=335,a=2,d=−3 , we get

S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]S

335

=

2

335

[2(2)+(335−1)(−3)]

S_{335}=\dfrac{335}{2}[4+(334)(-3)]S

335

=

2

335

[4+(334)(−3)]

S_{335}=\dfrac{335}{2}[4-1002]S

335

=

2

335

[4−1002]

S_{335}=\dfrac{335}{2}(-998)S

335

=

2

335

(−998)

On further simplification, we get

S_{335}=335\times (-499)S

335

=335×(−499)

S_{335}=-167165S

335

=−167165

Therefore, the sum of the first 335 terms in the given sequence is -167165.


Related Questions

Solve the inequality.
4 <-3x – 1= 9
[?]
< x <
[

Answers

Hi ;]

4 ≤ -3x - 1 ≤ 9

-3x - 1 ≥ 4  / + 1

-3x ≥ 5  / : (-3)

x ≥ -⁵/₃

-3x - 1 ≤ 9  / + 1

-3x ≤ 10  / : (-3)

x ≤ -¹⁰/₃

-⁵/₃ ≤ x ≤ -¹⁰/₃

Make the number 16 using six "1"s. Example: Make the number 18 using six "1"s. A: (11-1-1)(1+1)= 18

Answers

(1+1)(1+1)^(1+1)=16
4^2=16

Please can you solve this questions for me!!
It's important ​

Answers

15:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{x^5y^6}{xy^2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{5-1}y^{6-2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^4y^4[/tex]

16:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{x^2y^5}{xy^4}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{2-1}y^{5-4}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto xy[/tex]

17;-

[tex]\\ \qquad\quad\sf\longmapsto \left(\dfrac{4x^5y}{16xy^4}\right)^3[/tex]

[tex]\\ \qquad\quad\sf\longmapsto (4^{1-2}x^{5-1}y^{1-4})^3[/tex]

[tex]\\ \qquad\quad\sf\longmapsto (4^{-1}x^4y^{-3})^3[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 4^{-3}x^{12}y^{-9}[/tex]

18:-

[tex]\\ \qquad\quad\sf\longmapsto \left(\dfrac{5x^3y}{20xy^5}\right)^4[/tex]

[tex]\\ \qquad\quad\sf\longmapsto (4^{-1}x^{2}y^{-4})^4[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 4^{-4}x^8y^{-16}[/tex]

19:-

[tex]\\ \qquad\quad\sf\longmapsto y^{-7}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{y^7}[/tex]

20:-

[tex]\\ \qquad\quad\sf\longmapsto 7^{-2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{7^2}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{49}[/tex]

21:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{x^{-5}}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^5[/tex]

22:-

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{2^{-4}}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 2^4[/tex]

[tex]\\ \qquad\quad\sf\longmapsto 16[/tex]

23:-

[tex]\\ \qquad\quad\sf\longmapsto x^5\times x^{-1}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{5-1}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^4[/tex]

24:-.

[tex]\\ \qquad\quad\sf\longmapsto x^{-6}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto \dfrac{1}{x^6}[/tex]

25:-

[tex]\\ \qquad\quad\sf\longmapsto x^9(x^{-7})[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^{9-7}[/tex]

[tex]\\ \qquad\quad\sf\longmapsto x^2[/tex]

Differentiate
[tex] \sqrt{x} + \frac{1}{5x} - 3[/tex]
with respect to their variable ​

Answers

[tex]\\ \tt\longmapsto \dfrac{d}{dx}\sqrt{x}+\dfrac{1}{5x}-3[/tex]

[tex]\\ \tt\longmapsto \dfrac{d}{dx}x^{\frac{1}{2}}+5x^{-1}-3[/tex]

Derivative of any constant is 0

[tex]\\ \tt\longmapsto \dfrac{d}{dx}x^{\frac{1}{2}}+5x^{-1}[/tex]

[tex]\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}[/tex]

[tex]\\ \tt\longmapsto \dfrac{1}{2}x^{\frac{-1}{2}}-5x^{-2}[/tex]

[tex]\\ \tt\longmapsto \dfrac{x}{2}^{\frac{-1}{2}}-\dfrac{1}{5x^2}[/tex]

[tex]\\ \tt\longmapsto -\sqrt{\dfrac{x}{2}}-\dfrac{1}{5x^2}[/tex]

5/8k=25
how do i do this?

Answers

Answer:

[tex] \frac{5}{8} k = 25 \\ \frac{5k}{8} = 25 \\ 5k = 25 \times 8 \\ 5k = 200 \\ k = \frac{200}{5} \\ k = 40[/tex]

I hope it helped U

stay safe stay happy

Answer:

k=1/40

Step-by-step explanation:

multiple both sides by 8k

5= 25×8k

simplify 25×8k to 200k

5=200k

divide both sides by 200

5/200=k

simplify 5/200 to 1/40

1/40= k

switch sides

k=1/40

Find the quotient. Round to the hundredths place.

99.466 divided by 14.8

Answers

Answer:

6.72

Step-by-step explanation:

I multiplied both numbers by 10 to make it easier in my opinion. That made the equation 994.66 x 148

Then, I divided it until i got to the thousandths place. Lastly, i just rounded making it 6.72

Please Help im being timed!!! Is this True or False

Answers

Answer:

True

Step-by-step explanation:

[tex]f(x)=y=-8x+5: exchanging\ x\ and\ y\\\\x=-8y+5\\\\8y=-x+5\\\\f^{-1}(x)=y=\dfrac{-x}{8}+\dfrac{5}{8} =g(x)\\\\\\[/tex]

The two functions are inverses.

The graph of y = 2x + 1 is:

True or False

Answers

Answer:

False

Step-by-step explanation:

We can already see that the y-intercept doesn’t matches with the inequality.

Therefore, it is false

Answer:

False

Step-by-step explanation:

If the graph represented y = 2x + 1, then the y-intercept would be 1. The slope is correct(-ish), the y-intercept is not.

I am a three-digit number
My second an last digit are the same
The product of the digit of the numbe one less than me is not zero
The number one less than me is divisible by 45


Please help me solve this riddle. Thank you.

Answers

Answer:

766?

Step-by-step explanation:

Answer and Step-by-step explanation:

Three Digit Number.

***

Second digit = Last digit

*xx

I multiplied 45 from numbers 1-23, with 22 being the maximum # to multiply to get a 3 digit number that is divisible by 45, and 3 being the minimum # to multiply to get a 3 digit number that is divisible by 45.

Now to check which number it is.

When you multiply 45 by 17, you get 765. This number is supposed to be 1 less than the riddle's number. It also has to have the last 2 digits be the same.

So, lets add one to 765 to see if we solved the riddle.

765 + 1 = 766

766 is the answer!

#teamtrees #PAW (Plant And Water)

I hope this helps!

8, 13, 18, 23 how to write out the sequence Nth term

Answers

Answer:

5n+3

Step-by-step explanation:

:)

Answer:

[tex]\alpha n=5n+3[/tex]

Step-by-step explanation:

Are 8x²y and -5yx2 like terms? Explain.

Answers

Answer:

In algebra, like terms are terms that have the same variables and powers. ... Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.

Answer:

These are not like terms.

Step-by-step explanation:

Although their variables are the same, the exponents are different.  LIke terms must have the same variables AND same exponents.  The first term's variables are: x raised to the second power times y, while the other term's variables are:  y times x times 2

2x ≠ x²

Simplify.


18 2+6(4+1) -2

Answers

Answer:

[tex]1)18 \times 2 + 6(4 + 1) - 2 \\ = 36 + 6 \times 5 - 2 \\ = 36 + 30 - 2 \\ 36 + 28 \\ = 64 \\ \\ thank \: you[/tex]

Answer:

18×2+6(4+1)-2

= 36+6×5-2

= 36+30-2

= 66-2

=64

Solve for x please will mark brainliest

Answers

Answer:

[tex]4y + 6y = 90 \\ 10y = 90 \\ y = 9 \\ thank \: you[/tex]

If 2^10 + 2^10 = 2^x, what's x?

Answers

Answer:

11

Step-by-step explanation:

2^10 + 2^10 = 2^x

1024 + 1024 = 2^x

2,048 = 2^x

x = 11

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]x = 11[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'...}}\\\\2^{10}+2^{10} = 2^x\\--------------\\\rightarrow 2^{10} = 1024\\\\\rightarrow 1024 + 1024 = 2^x\\\\\rightarrow 2048 = 2 ^x\\\\\rightarrow log(2^x)=log(2048)\\\\\rightarrow xlog(2)=log(2048)\\\\\rightarrow \frac{log(2)}{log(2)} =\frac{log(2048)}{log(2)}\\\\\rightarrow x = \frac{log(2048)}{log(2)}\\\\\rightarrow \boxed{x = 11}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Which of the following is an irrational number? How do you know? Use key words and definitions to explain your answer choice.
1632
0.25
0.0300300030000…
0

Answers

Answer:

0.0300300030000...

Step-by-step explanation:

An irrational number has endless non-repeating digits to the right of the decimal point. They can be written as decimals, but not as fractions.

1632 can be written as 3264/2

0.25 can be written as 1/4

0 could be written as 0/0

but 0.0300300030000 cannot be written as a fraction, and it satisfies the condition of an irrational number having endless non-repeating digits to the right of the decimal point.

Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.

Answers

y=x+5, or you could but y=1x+5 it’s the same thing

help pls its ez :))))))))))))))))

Answers

Answer:

Yes

Step-by-step explanation:

6 × 18.75 = 112.50

8 × 18.75 = 150.00

11 × 18.75 = 206.25

HELP PLEASE I NEED THIS ONE!!!

If n/30 lies between 1/5 and 1/3, what are all the possible values of n if n is a whole number?

I’ll give brainliest

Answers

Answer:

7, 8, 9

Step-by-step explanation:

1/5 = 6/30

1/3 = 10/30

2(3m+6n) + 3(5m-2n)+ 5(-6m+n) ​

Answers

Answer:

[tex]2(3m + 6n) + 3(5m - 2n) + 5( - 6m + n) \\ [/tex]

open the brackets:

[tex] = (6m + 12n) + (15m - 6n) + ( - 30m + 5n) \\ [/tex]

group the coefficients of m and n in their brackets:

[tex] = (6 + 15 - 30)m + (12 - 6 + 5)n \\ [/tex]

then operate the brackets:

[tex] = - 9m + 11n[/tex]

What is the slope of the line represented​

Answers

Hi

the slope is the part before. " X"

dont forget the sign !

have fun !

please help with this one

Answers

A. is the correct answer

Answer:

A

Step-by-step explanation:

(x-3)(2x+1)= (due to FOIL(First Outer Inner Last)) (First)2x^2-(Outer+Inner)5x-(Last)3. 2x^2-5x-3 is what A says, so A is the answer.

7
If 8(x - 2y) = 16x, then what is x in terms of y?


Answers

Answer: y = -1/2x

8(x - 2y) = 16x

8x -16y = 16x

-16y      = 16x-8x

-16y      = 8x

-16y/-16= 8x/-16

        y = -1/2x

Find the midpoint of points A(9, 2) and B(6,-4) graphically.
Plot the line segment AB by clicking twice on the graph.
Start over
10
9
8
2 6 5
4
3
2
6
-10
--
-5
7
3
2
CH
القومي
-
u
6
7
7
S
9
10
-2
-3 4
-5
9
-7
-8
-10

Answers

Answer:

Mid point of A(9,2) and B(6,44) is (7.5, -1)

Step-by-step explanation:

I. If mid point = [tex]\frac{x_{a} +x_{b} }{2}[/tex], [tex]\frac{y_{a}+ y_{b} }{2}[/tex]

 So (x) = (9 + 6) / 2 = 7.5

       (y) = (2 + (-4)) / 2 = -1

So (x,y) = (7.5, -1)        

Leave more question below, I don't understand you question well.

Help me pls i have to finish my homework i have more questions to post too

Answers

Answer:

17) 19

19) 8

Step-by-step explanation:

17)

(6 +6² -4)÷2

(6 +36 -4)÷2

(38)÷2

19

19)

3³ ÷3 - 1

27 ÷3 -1

9 -1

8

Simplify.

What is the answer?

Answers

Answer:

81[tex]y^{8}[/tex][tex]z^{4}[/tex]

Step-by-step explanation:

What is the volume of the following rectangula
prism?
4
units
3
23
units
4

Answers

SORRYYYYYYYYYYYYYYY I DONT KNOWWWWW

The track team needs new uniforms. the students plan to sell candies. the students find three companies for 44.80. company c charges

Answers

Answer:  Answer:

Company C

Step-by-step explanation:

Company A sells 12 tigers for $33.24.

Cost per tiger = $33.34 / 12

= $2.78

Company B sells 16 tigers for $44.80. Company

Cost per tiger = $44.80 / 16

= $2.8

C charges $41.10 for 15 tigers.

Cost per tiger = $41.10 / 15

= $2.74

The company that has the best buy is company C that charges $2.74 per tiger

Brainliest please

anyone know this question: 16) -8(-21 - 2) - 6​

Answers

Answer:178

Step-by-step explanation:

distribute, multiply -8 with - 21 and -2 . that would get you 168 + 16 - 6. add the 168 and 16, it equals 184, then subtracts it with a 6.

Which equation has the solution x=-4? a 2(x-4)=16 b 3x+6-2x=-2 c 1/4x+4=3 d(x+6)3=-6 need help plz

Answers

Answer:

C: 1/4x + 4 = 3

Step-by-step explanation:

1/4x + 4 = 3

1/4x = 3 - 4

x = - 4

Thus, option c gives out the solution x = - 4.

Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?
2.4 hours
2.5 hours
3.0 hours
4.0 hours

The answer is supposedly 2.4 hours, but how ?? Please explain. Thanks!

Answers

In one hour Randy cleans at least 1/4 of the offices and in one hour Trey cleans at least 1/6 of the offices.

Working together they would clean at least 1/4 + 1/6 = 5/12 of the offices.

Let x be the greatest amount of time it would take them to clean the offices together. Then we can write the following equation:

5x/12=1

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