Question

Find the third term of the geometric sequence when a^1=1/4 and r=−2

Answer 1

The answer is 1

Explanation:

Since the sequence is a geometric sequence

For an nth term in a geometric sequence

`A(n) = a ({r})^(n - 1)`

where n is the number of terms

a is the first term

r is the common ratio

From the question

a = 1/4

r = - 2

Since we are finding the third term

n = 3

So the third term of the sequence is

`A(3) = (1)/(4) ({ - 2})^(3 - 1)`

`A(3) = (1)/(4)( { - 2})^(2)`

`A(3) = (1)/(4) * 4`

We have the final answer as

A(3) = 1

Hope this helps you