Chapter 12.2, Problem 45E

To determine

To calculate:

  $n^{th}$ term in the sequence in terms of $n$ .

Answer to Problem 45E

  $n^{th}$ term in the sequence in terms of $n$ is $a_n=\left(-2\right){\left(-3\right)}^{n-1}$ .

Explanation of Solution

Given information:

  $a_1=-2,a_n=-3a_{n-1}$ where $n>1$

Calculation:

It is given that first term in a geometric series $a_1=-2$

Every subsequent term is defined by $a_n=-3a_{n-1}$

The common ratio for the given series is,

  $a_n=a_1{r}^{n-1}$

Therefore, the $n^{th}$ term of the series is,

  $\begin{array}{l}{a}_n=a_1{r}^{n-1}\\ a_n=\left(-2\right){\left(-3\right)}^{n-1}\end{array}$

Thus, $n^{th}$ term in the sequence in terms of $n$ is $a_n=\left(-2\right){\left(-3\right)}^{n-1}$ .