Question

Find the sum of the following arithmetic progressions:
$1,3,5,7,....$ to $12$ terms

Answer 1

Given A.P is

$1,3,5,7,...\dots ..$

Number of terms of A.P is $n=12$

First term of this A.P is $a_1=1$

Second term of this A.P is $a_2=3$

Common difference $d=a_2-a_1=3-1=2$

We know that sum of $n$ term of an A.P is given by:

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

$S_{12}=\frac{12}{2}[2\times 1+(12-1)\times 2)]$

$S_{12}=6[2+22]$

$S_{12}=144$

Hence, the sum of given A.P is $144$.