Final answer:
To find the first term of the geometric series, we can use the formula for the sum of a geometric series. Given the sum of the first 3 terms as 171 and the common ratio as 2/3, substituting these values into the formula, we can solve for the first term. The first term of the series is 27.
Step-by-step explanation:
To find the first term of the geometric series, we can use the formula for the sum of a geometric series:
S = a(1 - r^n)/(1 - r)
Where S is the sum of the first n terms, a is the first term, and r is the common ratio.
Given that the sum of the first 3 terms is 171 and the common ratio is 2/3, we can substitute these values into the formula:
171 = a(1 - (2/3)^3)/(1 - 2/3)
Simplifying this equation, we get:
171 = a(1 - 8/27)/(1/3)
171 = a(19/27)/(1/3)
171 = a(19/27)/(1/3)
Now, we can solve for a:
a = 171 * (1/3) * (27/19) = 9 * 3 = 27
Therefore, the first term of the series is 27.