Question

The first term of a geometric sequence is 48, and the 5th term of the sequence is 243/16.

What are the geometric means between these terms?

Enter your answer by filling in the boxes to correctly complete the geometric sequence. Enter any fractions as simplified fractions.

48,_,_,_,243/16

Answer 1

Explanation:

The geometric formula is
`a_(n) =a_(1) * r^(n-1)` where a1 is the first term and
`a_(n)` is the term at the nth position and r is the ratio.

Since 48 is the first term and 243/26 is the fifth term, we get the equation

`(243)/(16) = 48*r^(5-1)`

thus r = 0.75

thus the three missing terms are 36, 27, 81/4