Question

The common ratio of a geometric series is \dfrac14

4
1
​
start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

Answer 1

128

Explanation:

Answer 2

The first term is 128

Explanation:

The common ratio of the geometric series is given as:

`r = (1)/(4)`

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

`s_n=(a_1(1-r^n))/(1-r)`

We put the common ratio, n=4 and equate to 170.

`(a_1(1-( (1)/(4) )^4))/(1- (1)/(4) ) = 170`

Simplify:

`(a_1(1- (1)/(256) ))/( (3)/(4) ) = 170`

`(255)/(256) a_1 = (3)/(4) * 170`

`(255)/(256) a_1 = (255)/(2)`

`(1)/(256) a_1 = (1)/(2)`

`a_1 = (1)/(2) * 256`

`a_1 = (1)/(2) * 256 = 128`