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 of the series?

Answer 1

`S_n=(b_1(q^n-1))/(q-1) \\q=(2)/(3) , b_1=x, n=3, S_n=171`

Let's find b₁

`171=(x(((2)/(3))^3-1) )/((2)/(3)-1 ) \\\\\\171=x*(-(19)/(27) )*(-3) \\171=(19)/(9) x\\x=171*(9)/(19) \\x=81`

Answer: b₁=81

Answer 2

81

Step-by-step 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