Question

Find each sum

$7+1-5-11-.....-299$

Short answer

The solution is$S_{52}=-7592$

Step-by-step solution

Given information

$7+1-5-11-.....-299$

Calculation

We have, $7+1-5-11-.....-299$

So, $a_1=7,d=-6,a_n=-299$

Now use formula

$$\begin{gathered} a_n=a_1+(n-1)d \\ \Rightarrow -299=7+(n-1)(-6) \\ \Rightarrow -299=7-6n+6 \\ \Rightarrow -6n=-312 \\ \Rightarrow n=52 \end{gathered}$$

To find sum $S_{52}$

role="math" localid="1649306434221" $$\begin{gathered} S_{52}=\frac{52}{2}[7+(-299\left)\right] \\ =-7592 \end{gathered}$$