Chapter 8.3, Problem 13E

a.

To determine

To find: rule for geometric sequence with given description.

Answer to Problem 13E

The nth term of GP with given description is $a_n=-3\cdot 5^{n-1}$ .

Explanation of Solution

Given information:

The first term of sequence is -3,

Each term is 5 time the previous term

Formula used:

n^th term of a GP is:

  $a_n=a{r}^{n-1}$

Where,

  $a$ =first term

  $r$ =common ratio

Recall that n^th term of a GP is:

  $a_n=a{r}^{n-1}$

Where,

  $a$ =first term

  $r$ =common ratio

By given condition,

  $\begin{array}{l}a=-3\\ r=5\end{array}$

So, the nth term of GP is:

  $\begin{array}{l}{a}_n=a{r}^{n-1}\\ \\ a_n=-3\cdot 5^{n-1}\end{array}$

The nth term of GP with given description is $a_n=-3\cdot 5^{n-1}$ .

b.

To determine

To find: rule for geometric sequence with given description.

Answer to Problem 13E

The nth term of GP with given description is $a_n=72\cdot {\left(\frac{1}{3}\right)}^{n-1}$ .

Explanation of Solution

Given information:

The first term of sequence is 72,

Each term is $\frac{1}{3}$ time the previous term

Formula used:

n^th term of a GP is:

  $a_n=a{r}^{n-1}$

Where,

  $a$ =first term

  $r$ =common ratio

Recall that n^th term of a GP is:

  $a_n=a{r}^{n-1}$

Where,

  $a$ =first term

  $r$ =common ratio

By given condition,

  $\begin{array}{l}a=72\\ r=\frac{1}{3}\end{array}$

So, the nth term of GP is:

  $\begin{array}{l}{a}_n=a{r}^{n-1}\\ \\ a_n=72\cdot {\left(\frac{1}{3}\right)}^{n-1}\end{array}$

The nth term of GP with given description is $a_n=72\cdot {\left(\frac{1}{3}\right)}^{n-1}$ .