Question

The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3. What is the first term?​

Answer 1

81

Explanation:

let the terms be a,ar,ar²

r=2/3

a+a(2/3)+a(2/3)²=171

multiply by 9

9a+6a+4a=171×9

19 a=171×9

a=(171×9)/(19)

a=9×9=81

Answer 2

The first term is 81

Explanation:

The common ratio is 2/3.

`r = (2)/(3) <1`

Sum of first n terms in GP =
`S_n=(a(1-r^n))/(1-r)`

The sum of the first 3 terms of a geometric series is 171

n=3

Substitute the values in the formula:

`S_3=(a(1-((2)/(3))^3)/(1-(2)/(3))`

`171=(a(1-((2)/(3))^3))/(1-(2)/(3))`

`171(1-(2)/(3))=a(1-((2)/(3))^3)`

`(171(1-(2)/(3)))/((1-((2)/(3))^3))=a`

`81=a`

Hence The first term is 81