Question

Find the sum of the following geometric series $1+2+4+$ ........ upto $10$ terms

Answer 1

It is given that the first term of G.P is $a_1=1$ and the second term is $a_2=2$, therefore,

$r=\frac{a_2}{a_1}=\frac{2}{1}=2$

We know that the formula for sum of $n$ terms of G.P is $S_n=\frac{a(r^n-1)}{r-1}$, where $a$ is the first term, $r$ is the common ratio.

In the given geometric series, the first term is $a=1$, the common ratio is $r=2$ and the number of terms are $n=10$, therefore,

$S_{10}=\frac{1(2^{10}-1)}{2-1}=\frac{1024-1}{1}=1023$

Hence, $S_{10}=1023$.