Question

In a G. P., the last term is $1024$ and the common ratio is $2$. Its ${20}^{th}$ term from the end is.

• A. $\frac{1}{1024}$
• B. $\frac{1}{256}$
• C. $512$
• D. $\frac{1}{512}$

Answer 1

The correct option is D

$\frac{1}{512}$

Explanation for the correct answer:

To find the ${20}^{th}$ term from the end is :

Given, that the last term is $1024$ and the common ratio is $2$ of a GP

Let us consider there are $n$ terms in the G.P,

We know the formula for $n^{th}$ term in the G.P is $t_n=a{r}^{n-1}$ where $a$ is the first term and $r$ is common ratio.

When we consider $1024$ as the first term then $\frac{1}{2}$ will be the common ratio.

So, ${20}^{th}$ term from the end is

$$\begin{gathered} t_{20}=1024{\left(\frac{1}{2}\right)}^{20-1} \\ {t}_{20}=1024{\left(\frac{1}{2}\right)}^{19} \\ {t}_{20}=\frac{1}{512} \end{gathered}$$

Hence, the correct option is D.