If 3rd term of a geometric progression is 1/9 and common multiple is 1/3, then what is the sum of first four terms of the geometric progression?

If 3rd term of a geometric progression is 1/9 and common multiple is 1/3, then what is the sum of first four terms of the geometric progression? Correct Answer 40/27

Given:

Geometric progression whose third term is 1/9 and common multiple is 1/3.

Formula used:

n^th term of geometric progression (G.P.) = a × r^n-1, where a = first term and r = common multiple

Sum of first ‘n’ terms of geometric progression (G.P.), S_n = a / , where r < 1, a = first term, r = common multiple

Calculation:

3^rd term = 1/9, r = 1/3

⇒ 1/9 = a × r^3-1

⇒ 1/9 = a × (1/3)²

⇒ 1/9 = a × 1/9

⇒ a = 1

Thus, a = 1, r = 1/3

⇒ Sum of first 4 terms = 1 × × {1/ }

⇒ × 3/2

⇒ (80/81) × (3/2)

⇒ 40/27