Question

How many terms of a geometric progression 2. 4. 8. 16. ...would add to 126​

Answer 1

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Answer 2

Given, Geometric progression 2,4,8,16..

$\therefore$ first term a=2, common ratio r=2

Given that the sum of GP $S_n=126$

We know, $S_n=\frac{a(r^n-1)}{r-1}$

$126=\frac{2(2^n-1)}{2-1}=2(2^n-1)\\\Rightarrow \frac{126}{2}=2^n-1=63\\\Rightarrow 2^n-1=63\\\Rightarrow 2^n=63+1=64=2^6$

Comparing, $n=6$

$\therefore$ 6 terms of a geometric progression 2. 4. 8. 16. ...would add to 126​.

To learn more about solving questions involving the sum of GP, click on the links below:

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