Question

Find the sum of the geometric series 3 + 6 + 12 + … + 1536.

Answer 1

r = 6 ÷ 3 = 2 

Tⁿ = ar^n-1 

⇒1536 = 3 × 2^n-1 

⇒1536 ÷ 3 = 2n ÷ 2 

⇒1536 ÷ 3 × 2 = 2ⁿ 

⇒1024 = 2ⁿ 

⇒2¹⁰ = 2ⁿ 

∴ n = 10

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 = 3 

r = 2 

n = 10 terms