Chapter 5 - The Integral - 5.1 Approximating and Computing Area - Exercises - Page 236: 32

a) 110 b) 25 c) 19

a) \begin{equation} \sum_{i=1}^{10}(4a_{i}+3)=4\sum_{i=1}^{10}a_{i}+\sum_{i=1}^{10}3=4\times20+3\times10=110\end{equation} b) \begin{equation} \sum_{i=2}^{10}a_{i}=\sum_{i=1}^{10}a_{i}-a_{1}=20-(-5)=25\end{equation} c) \begin{equation} \sum_{i=1}^{10}(2a_{i}-3b_{i})=2\sum_{i=1}^{10}a_{i}-3\sum_{i=1}^{10}b_{i}=2\times20-3\times7=19\end{equation}