Answer:
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
