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

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed