Chapter 4, Problem 17CR

To determine

To Calculate : To calculate the 30^th term of the arithmetic sequence.

Answer to Problem 17CR

The 30^th term of the arithmetic sequence $-9,-6,-3,0,\mathrm{...}$ is $a_{30}=78$ .

Explanation of Solution

Given information : Given arithmetic sequence is $-9,-6,-3,0,\mathrm{...}$ .

By inspection of given sequence, observe that each term of the arithmetic sequence is increasing by multiple of $3$ starting from $-9$ .

Then, n^th term of this sequence will be

  $\begin{array}{c}{a}_n=-9+3\left(n-1\right)\\ =-9+3n-3\\ =-12+3n\end{array}$ .

Therefore, to find the 30^th term, we just need to put $n=30$ .

  $\begin{array}{c}{a}_{30}=-12+3\times 30\\ =-12+90\\ =78\end{array}$

Thus, the 30^th term of the arithmetic sequence $-9,-6,-3,0,\mathrm{...}$ is $a_{30}=78$ .