Insert three geometric means between 2 and 81/8

In a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:

Recall:

Given a geometric sequence, 2 . . . 81/8, with three other terms in the middle, first, find the value of r.

Thus:

First Term:

Fifth Term:

a = 2

n = 5

r = ?

T5 = 81/8

Find the three geometric means between 2 and 81/8.

a = 2

r = 3/2

Therefore, in a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:

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Step-by-step explanation:

The nth term of a geometric sequence is expressed as Tn = where;

a is the first term

r is the common ratio

n is the number of terms

Since we are to insert three geometric means between 2 and 81/8, the total number of terms in the sequence will be 5 terms as shown;

2, a, b, c, 81/8

a, b, and c are the 3 geometric mean to be inserted

T1 = = 2

T1 = a = 2....(1)

T5=

T5 = = 81/8... (2)

Dividing equation 1 by 2 we have;

Given a =2 and r = 3/2;

Therefore the three geometric means are 3, 9/2 and 27/4