Chapter 9.4, Problem 1LC

Solution

To find: The sum of the finite arithmetic series, $4+7+10+13+16+19+22$ .

The sum of the series is $91$ .

Given information:

The series, $4+7+10+13+16+19+22$ .

Formula used:

The sum of n terms of an arithmetic series $a_1+a_2+\mathrm{...}+a_n$ with fist term $a_1$ and last $a_n$ is given as $S_n=\frac{n}{2}\left(a_1+a_n\right)$ .

Calculation:

The given series has 7 terms with first term $a_1=4$ and the last term $a_7=22$ .

Now, use the formula $S_n=\frac{n}{2}\left(a_1+a_n\right)$ to find the sum of 7 terms of the series.

  $\begin{array}{c}{S}_7=\frac{7}{2}\left(a_1+a_7\right)\\ =\frac{7}{2}\left(4+22\right)\\ =7\cdot 13\\ =91\end{array}$

Conclusion:

The sum of the series is $91$ .