Question

A geometric series has t1 = 3 and r = 2. If tn = 96. What does n equal in this problem?

What is the special name given to the terms between 3 and 96 in this problem?

Answer 1

You are given that a = 3 and r = 2
so
tn = ar^(n-1)
96 = 3(2^(n-1)
32 = 2^(n-1)
2^5 = 2^(n-1)
n-1 = 5
n = 6

3, 6, 12, 24, 48, 96
terms in between are called geometric means

Answer 2

Thanks!