The sum of the first 333 terms of a geometric series is 171171171 and the common ratio is / dfrac23

3

2



start fraction, 2, divided by, 3, end fraction.

What is the first term of the series?

The first term of the series is 81

Step-by-step explanation:

The sum of the nth term of a geometric sequence is expressed as shown;

Sn = a (1-rⁿ) / 1-r for r<1

a is the first term

r is the common ratio

n is the number of terms

Given Sn = 171

r = 2/3

n = 3

a = ?

Substituting the values in the equation

171 = a (1 - (2/3) ³) / 1-2/3

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

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

171 = a * 19/27 * 3/1

171 = a * 19/9

Cross multiplying

171*9 = 19a

1539 = 19a

a = 1539/19

a = 81

The first term is 81