Precalculus (6th Edition) Blitzer

The first three terms of $\sum\limits_{i=1}^{17}{(5i+3)}$ are 8,13, and 18. The common difference is 5.
To find the first three terms, we will substitute the value of $i=1,2\text{ and }3$ in the given summation. For $i=1$ \begin{align} & 5i+3=(5\times 1+3) \\ & =(5+3) \\ & =8 \end{align} For $i=2$ \begin{align} & 5i+3=(5\times 2+3) \\ & =(10+3) \\ & =13 \end{align} For $i=3$ \begin{align} & 5i+3=(5\times 3+3) \\ & =(15+3) \\ & =18 \end{align} By evaluating the first three terms, we can see that ${{a}_{1}}=8$ and the common difference is $d=13-8=5$.