Question

Find the sum of the following arithmetic progressions:
$-26,-24,-22,....$ to $36$ terms.

Answer 1

Given A.P is

$-26,-24,-22,...\dots ..$

number of terms of A.P is $n=36$

first term of this A.P is $a_1=-26$

second term of this A.P is $a_2=-24$

common difference

$d=a_2-a_1=-24-(-26)=2$

we know that sum of n term of an A.P is given by

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

$⟹S_{36}=\frac{36}{2}[2\times -26+(36-1)\times 2)]$

$⟹S_{36}=18[-52+35\times 2)]$

$⟹S_{36}=18[-52+70)]$

$⟹S_{36}=18[18]$

$⟹S_{36}=324$

hence the sum of $36$ terms of given A.P is $324$