Answer
The first three terms of $\sum\limits_{i=1}^{17}{(5i+3)}$ are 8,13, and 18. The common difference is 5.
Work Step by Step
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 $d=13-8=5$.
