Question

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

Answer 1

Answer:

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

Answer 2

$S_n=\dfrac{b_1(q^n-1)}{q-1} \\q=\dfrac{2}{3} , b_1=x, n=3, S_n=171$

Let's find b₁

$171=\dfrac{x((\dfrac{2}{3})^3-1) }{\dfrac{2}{3}-1 } \\\\\\171=x*(-\dfrac{19}{27} )*(-3) \\171=\dfrac{19}{9} x\\x=171*\dfrac{9}{19} \\x=81$

Answer: b₁=81