Chapter 11.2, Problem 59PPS

To determine

Find the sum of ${\displaystyle \sum _{k=5}^{k=16}2k+6}$

Answer to Problem 59PPS

Sum of the series is 324.

Explanation of Solution

Given:

Find the sum of ${\displaystyle \sum _{k=5}^{k=16}2k+6}$

Concept Used:

K = 6 should be the first term and k = 16 should be the last term.

Calculation:

  $\begin{array}{l}{\displaystyle \sum _{k=5}^{k=16}2k+6};k=5\\ 2k+6=2·5+6=16\\ a_5=16\end{array}$

  $\begin{array}{l}{\displaystyle \sum _{k=5}^{k=16}2k+6};k=16\\ 2k+6=2·16+6=38\\ a_{16}=38\end{array}$

  $\begin{array}{l}{a}_5=16;a_{16}=38,n=12\\ {\text{S}}_{10}=\frac{n}{2}(a_4+a_{13})\\ {\text{S}}_{10}=\frac{12}{2}(16+38)\\ {\text{S}}_{10}=6·54=324\end{array}$

Thus, sum of the series is 324.