Question

What is the sum of the first $7$ terms of a geometric progression whose first term is $1$ and $4^{th}$ terms is $8$?

• A. $129$
• B. $128$
• C. $127$
• D. $Noneofthese$

Answer 1

The correct option is C $127$

Given that,

$a=1,a_4=8$

$\frac{a{r}^3}{a}=\frac{8}{1}$

$r=2$

$Sumoffirst7term-$

$S_7=\frac{1(r^7-1)}{2-1}$

$S_7=1(128-1)$

$S_7=127$

Hence, this is the answer.