Question

Find the indicated term of the given geometric sequence. Select your answer choice and then click Submit to see if you are correct.

Identify the 10th term of the geometric sequence 2, 8, 32 …

Answer 1

`b_(10)=2^(19)`

Explanation:

Given the geometric sequence
`2,\ 8,\ 32,\ ...`

In this sequence,

`b_1=2\\ \\b_2=8\\ \\b_3=32\\ \\...`

Find the common ratio r:

`r=(b_2)/(b_1)=(8)/(2)=4`

or

`r=(b_3)/(b_2)=(32)/(8)=4`

Use formula for the
`n^(th)` term:

`b_n=b_1\cdot r^(n-1),`

so

`b_(10)=2\cdot 4^(10-1)\\ \\b_(10)=2\cdot 4^9\\ \\b_(10)=2\cdot 2^(18)\\ \\b_(10)=2^(19)`