Find the sum of the geometric series 3 + 6 + 12 + … + 1536.
Tn represents the nth term of a G.P. series.
r = 6 ÷ 3 = 2
Tn = arn-1
⇒1536 = 3 × 2n-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, , when r>1. ‘Sn’ represents the sum of the G.P. series upto 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
∴
⇒
⇒
∴