Question

In a geometric progression the first term, the last term and the common ratio are $1,64$ and $2$ respectively. What is the sum of all terms of the progression.

• A. $123$
• B. $126$
• C. $124$
• D. $127$

Answer 1

The correct option is D $127$

We have $a=1,r=2,l=64$

$l=a{r}^{n-1}$

$64=1(2{)}^{n-1}$

$⟹n=7$

So, we have,

$1,2,4,8,16,32,64$

Sum of the series

$=\frac{a(r^n-1)}{r-1}$

$=\frac{1(2^7-1)}{7-1}=127$