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?

81

Step-by-step explanation:

The formula for calculating the sum of geometric series varies depending on the value of its common ratio.

Given the common ratio to be 2/3 which is less than 1, the formula to be used is given as;

Sn = a (1-rⁿ) / 1-r

n is the number of terms of the series

a is the first term

r is the common ratio.

Sn is the sum of the series

Given n = 3, r = 2/3 and Sn = 171,

a=?

Substituting this values in the formula we have;

171 = a{1 - (2/3) ³}/1-2/3

171 = a{1-8/27} / (1/3)

171 = a (19/27) / (1/3)

171 = 19a/27 * 3/1

171 = 57a/27

57a = 171*27

57a = 4,617

a = 4,617/57

a = 81

The first term of the series is 81