Question

If the first term of a GP is $729$ and $7^{th}$ term is $64$, then the sum of its first seven terms is

• A. $2187$
• B. $2059$
• C. $1458$
• D. $2123$
• E. $1995$

Answer 1

Answer: (B)

$2059$

Given, first term of a GP is $a=729$
and $7^{th}$ term, $a_7=a{r}^6=64$
$\Rightarrow 729r^6=64$
$\Rightarrow r^6={\left(\frac{2}{3}\right)}^6$
$\Rightarrow r=\frac{2}{3}=$ Common ratio
Therefore, $a_1+a_2+a_3+a_4+a_5+a_6+a_7$
$=$ Sum of the first seven terms
$=\frac{a(1-r^7)}{1-r}=\frac{729\{1-{\left(\frac{2}{3}\right)}^7\}}{1-\frac{2}{3}}$
$=2059$