Chapter 7.9, Problem 46PFA

To determine

To find the 8^th term of the given sequence.

Answer to Problem 46PFA

  $a_8=3.953125$ & option C is correct.

Explanation of Solution

Given:

  $64768,16192,4048,1012,\mathrm{.........}$

Concept used:

The n^th term of a geometric sequence with first term ‘a’ and common ratio ‘r’ is

  $a_n=a{r}^{n-1}$

Calculation:

  $64768,16192,4048,1012,\mathrm{.........}$

Given sequence is a geometric sequence with

  $a=64768,r=\frac{16192}{64768}=\frac{1}{4}$

Therefore 8^th term is,

  $\begin{array}{l}{a}_8=a{r}^7\\ =64768{\left(\frac{1}{4}\right)}^7\\ =\frac{64768}{16384}\\ =3.953125\end{array}$

Hence option C is correct.