Find the sum of the first twenty terms

Algebra Level 2

The 6 t h 6^{th} term and 1 5 t h 15^{th} term of a geometric progression are 192 192 and 98304 98304 , respectively. Find the sum of the first 20 20 terms of this geometric progression.


The answer is 6291450.

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1 solution

Md Mehedi Hasan
Nov 11, 2017

Here, a r 5 = 192 a r 14 = 98304 ar^5=192\\ar^{14}=98304

Solving that a = 6 , r = 2 a=6,r=2

The summation of 1st 20th term is a ( r 20 − 1 ) r − 1 = 6 ( 2 20 − 1 ) 2 − 1 = 6291450 \frac{a(r^{20}-1)}{r-1}=\frac{6(2^{20}-1)}{2-1}=\boxed{6291450}

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