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

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

Answer:

The first term is 81

Step-by-step explanation:

The common ratio is 2/3.

$r = \frac{2}{3}$

Sum of first n terms in GP = $S_n=\frac{a(1-r^n)}{1-r}$

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

n=3

Substitute the values in the formula:

$S_3=\frac{a(1-(\frac{2}{3})^3}{1-\frac{2}{3}}$

$171=\frac{a(1-(\frac{2}{3})^3)}{1-\frac{2}{3}}$

$171(1-\frac{2}{3})=a(1-(\frac{2}{3})^3)$

$\frac{171(1-\frac{2}{3})}{(1-(\frac{2}{3})^3)}=a$

$81=a$

Hence The first term is 81