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