Question

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

Answer 1

Sum of a G.P. series is represented by the formula, S_n = a\(\frac{r^n - 1}{r-1}\), when r>1. 

‘S_n’ represents the sum of the G.P. series up to nth terms, 

‘a’ represents the first term, 

‘r’ represents the common ratio and 

‘n’ represents the number of terms.

Here, 

a = 2 

r = (ratio between the n term and n-1 term) 6 ÷ 2 = 3 

S_n = 728

∴ 6 terms must be taken to reach the desired answer.