Q9 of 104 Page 457

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


∴


⇒


⇒


∴


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