Write an equation to fond the nth term of each sequence. Then find a9. 5,20,80

Answer: a₉ = 327,680

Step-by-step explanation:

This seems to be a geometric sequence.

The recursive relation for this type of sequence is:

aₙ = aₙ₋₁*r

Where r is a constant.

Then we also have:

aₙ/aₙ₋₁ = r.

then we can find the value of r if we take the quotient of different consecutive terms, for example, the quotient of the second and firs term is:

r = 20/5 = 4

And the quotient between the third and second term is:

r = 80/20 = 4

Then we can conclude that r  = 4.

And also, the n-th term of this sequence can be written as:

aₙ = a₁*r^(n - 1)

such that:

a₁ = 5

r = 4

Then the n-th term of this sequence is:

aₙ = 5*(4)^(n - 1)

Then the term a₉ can be found if we just replace n by 9 in the above equation:

a₉ = 5*(4)^(9 - 1) = 5*(4)^(8) = 327,580

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