Answer:
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
