Correct Answer - Option 2 : 3827.03
Given:
The sum to infinity of a geometric progression is 39/2
Calculation:
Let the first term and common ratio of the geometric progression be a and r respectively
⇒ (a/1 - r) = 39/2 ------(1)
⇒ (a2/1 - r2) = 253.5 = 507/2 ------(2)
⇒ (a/1 - r)2 = (39/2)2 ------(3) (squaring (1) on both sides)
⇒ Dividing (2) by (3) and simplifying
⇒ r = 1/5, a = (39/2) × (1 - r) = 78/5
⇒ Sum of the cubes of the terms of the geometric progression
⇒ a3/(1 - r3) = (78 × 78 × 78)/124 = 3827.03 which is > 1000
∴ The required result will be 3827.03.