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# A sequence has a common ratio of 3/2 and f(5) = 81. Which explicit formula represents the sequence?

f(x) = 24

f(x) = 16

f(x) = 24

f(x) = 16

**Solution:**

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

The nth term of a geometric sequence is given by a_{n}=ar^{n-1}

where r is the common ratio between successive terms.

Given, f(5) = 81

Common ratio, r = 3/2

f(1) = a

f(2) = a(3/2)

f(3) = a(3/2)^{2}

f(4) = a(3/2)^{3}

f(5) = a(3/2)^{4}

We know f(5) = 81

So, a(3/2)^{4} = 81

a(81/16) = 81

a = 16

Thus, the n^{th} term can be found as f(n) = 16(3/2)^{n-1}

## A sequence has a common ratio of 3/2 and f(5) = 81. Which explicit formula represents the sequence?

**Summary:**

A sequence has a common ratio of 3/2 and f(5) = 81. The explicit formula that represents the sequence is f(n) = 16(3/2)^{n-1}

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