Question

Find the sum of the AP:$-37,-33,-29,...$ upto $12$ terms.

Answer 1

Find the sum of the AP:

We know that the sum of first $n$ terms of an AP is

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Where $a=$ first term and $d=$ common difference

We have, $-37,-33,-29,...$ upto 12 terms

Here,$a=-37,d=-33+37=4\text{and}n=12$

$\begin{array}{rcl}& \Rightarrow & S_{12}=\frac{12}{2}[2\times (-37)+(12-1)\times 4]\\ & =& 6[-74+11\times 4]\\ & =& 6[-74+44]\\ & =& 6\times (-30)\\ & =& -180\end{array}$

Hence, the required answer is $-180$.