Chapter 11.3, Problem 30WE

To determine

To calculate:

The following sequence is arithmetic, geometric or neither and the formula for $n^{th}$ term:

  $-17,-11,-5,1,\mathrm{...}$

Answer to Problem 30WE

The sequence is arithmetic sequence and formula for $n^{th}$ term is $a_n=-23+6n$

Explanation of Solution

Given information:

  $-17,-11,-5,1,\mathrm{...}$

Calculation:

Check the common difference first to categorize the given sequence into arithmetic, geometric or neither:

  $\begin{array}{l}{a}_1=-17\\ a_2=-11\\ a_3=-5\\ a_4=1\end{array}$

Now, the common difference is calculated as:

  $\begin{array}{l}d=a_2-a_1=-11+17=6\\ d=a_3-a_2=-5+11=6\\ d=a_4-a_3=1+5=6\end{array}$

Therefore, the given sequence is arithmetic sequence.

Now, the formula for $n^{th}$ term is calculated as:

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ a_n=-17+\left(n-1\right)6\\ a_n=-17+6n-6\\ a_n=-23+6n\end{array}$