Chapter 8.3, Problem 16E

To determine

To find: rule for nth term of sequence and $a_7$ term.

Answer to Problem 16E

The nth term of GP with given description is $a_n=6\cdot 4^{n-1}$ .

The value of $a_7$ term is 24576.

Explanation of Solution

Given information:

The sequence:

  $6,24,96,384,\mathrm{.....}$

Formula used:

n^th term of a GP is:

  $a_n=a{r}^{n-1}$

Where,

  $a$ =first term

  $r$ =common ratio

  $6,24,96,384,\mathrm{.....}$

Recall that n^th term of a GP is:

  $a_n=a{r}^{n-1}$

Where,

  $a$ =first term

  $r$ =common ratio

  $\begin{array}{l}r=\frac{a_2}{a_1}\\ \\ r=\frac{24}{6}\\ \\ r=4\end{array}$

By given condition,

  $\begin{array}{l}a=6\\ r=4\end{array}$

So, the nth term of GP is:

  $\begin{array}{l}{a}_n=a{r}^{n-1}\\ \\ a_n=6\cdot 4^{n-1}\end{array}$

The nth term of GP with given description is $a_n=6\cdot 4^{n-1}$ .

The value of $a_7$ term is,

  $n=7$

  $\begin{array}{l}{a}_n=6\cdot 4^{n-1}\\ \\ a_7=6\cdot 4^{7-1}\\ \\ a_7=6\cdot 4^{7-1}\\ \\ a_7=6\cdot 4096\end{array}$

  $a_7=24576$

The value of $a_7$ term is 24576.