Chapter 14.7, Problem 4MRE

To determine

To find:Whether the sequence is arithmetic or geometric and then find the specified term of the sequence.

Answer to Problem 4MRE

The given series is an arithmetic progression and it ${15}^{\text{th}}$ term is $-79$ .

Explanation of Solution

Given: $5,-1,-7,\mathrm{.......},t_{15}$ .

Check from common difference.

  $\begin{array}{c}-1-5=-7-\left(-1\right)\\ -6=-7+1\\ -6=-6\end{array}$

The common difference is same. So, the sequence is an arithmetic progression.

The expression for the $n^{\text{th}}$ term of an arithmetic sequence is given by.

  $a_n=a_1+\left(n-1\right)d$

Substitute the values in the above expression.

  $\begin{array}{c}{a}_{15}=5+\left(15-1\right)\left(-6\right)\\ =5+14\left(-6\right)\\ =-79\end{array}$

Therefore, the given series is an arithmetic progression and it ${15}^{\text{th}}$ term is $-79$ .