Question

How many terms of the series 2 + 6 + 18 + …. Must be taken to make the sum equal to 728?

Answer 1

Given:

Sum of GP = 728

Where, a = 2, r = 6/2 = 3, n = ?

By using the formula,

Sum of GP for n terms = a(rⁿ – 1 )/(r – 1)

728 = 2 (3ⁿ – 1)/(3 - 1)

728 = 2 (3ⁿ – 1)/2

728 = 3ⁿ – 1

729 = 3ⁿ

3⁶ = 3ⁿ

6 = n

∴ 6 terms are required to make a sum equal to 728