Question

Find the sum of the first $8$ terms of $3,6,12,24,.........$

• A. $765$
• B. $769$
• C. $786$
• D. $784$

Answer 1

The correct option is A $765$

sum of first $8$ terms of $3,6,12,\mathrm{24......}$

First-term $=3$

$Commonratio=\frac{secondterm}{firstterm}$

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

Now nth term of a G.P $a{r}^{n-1}$

$\therefore$ $8^{th}$ term

$\Rightarrow a_8=a{r}^{n-1}$

$=a\times r^{8-1}$

$=3\times 2^7$

$=3\times 2^5\times 2^2$

$=3\times 32\times 4$

$=32\times 12$

$\Rightarrow a_8=384$

$s_8=\frac{3\times (2^8-1)}{2-1}=3\times (2^8-1)$

$S_8=765$.......(A)