Question

Find each sum

$73+78+83+88+...+558$

Short answer

The solution is$S_{98}=30919$

Step-by-step solution

Given information

$73+78+83+88+...+558$

Calculation

We have, $73+78+83+88+...+558$

So, $a_1=73,d=5,a_n=558$

Now use formula,

$$\begin{gathered} a_n=a_1+(n-1)d \\ \Rightarrow 558=73+(n-1)5 \\ \Rightarrow 558=73+5n-5 \\ \Rightarrow 5n=490 \\ \Rightarrow n=98 \end{gathered}$$

To find sum $S_{98}$

$$\begin{gathered} S_{98}=\frac{98}{2}(73+558) \\ =30919 \end{gathered}$$