Question

Find the sum of the first fifteen terms of the series:

Answer 1

The sum of the first fifteen terms of the series is 98303

Explanation:

Given that the series is 3,6,12,24,.....

We need to determine the sum of the first terms of the series.

Common difference (r):

$r=\frac{6}{3} =2$

Hence, the common difference between is 2

The sum of the series can be determined using the formula,

$S_{n}=\frac{a_{1}\left(r^{n}-1\right)}{r-1}$

Substituting $a_1=3$ , $n=15$ and $r=2$, we get,

$S_{15}= \frac{3(2)^{15}-1}{2-1}$

Hence, simplifying the terms, we get,

$S_{15}= \frac{3(32768)-1}{2-1}$

$S_{15}= \frac{98304-1}{1}$

$S_{15}= 98303$

Thus, the sum of the first fifteen terms of the series is 98303