Question

Find the number of terms in the G.P 6,12, 24 ... 1536.

• A. 8
• B. 10
• C. 9
• D. 6

Answer 1

The correct option is C

9

Let 1536 be the $n^{\text{th}}$ term

Then, $a=6,ar=12,a{r}^2=24,a{r}^{n-1}=1536.$

$\Rightarrow r=\frac{ar}{a}=\frac{12}{6}=2$

$a{r}^{n-1}=1536$

$\Rightarrow 6\times (2{)}^{n-1}=1536$

$\Rightarrow (2{)}^{n-1}=256$

$\Rightarrow 2^{n-1}=2^8$

$\Rightarrow n-1=8$

$\Rightarrow n=9$

So, the total number of terms in the given G.P is 9.