Question

Without actual addition find the value of the following expression
1 + 3 + 5 + 7 + 9 + 11 + 13

Answer 1

Given expression, $1+3+5+7+9+11+13$ is in AP.

$T_1=a=1$

$T_2=3$

Common difference, $d=T_2-T_1=3-1=2$

So, we have $a=1,d=2,n=7$, to find the sum.

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

$S_7=\frac{7}{2}\left(2\right(1)+(7-1\left)2\right)$

$S_7=\frac{7}{2}\left(14\right)=7\times 7$

$S_7=49$

This is the sum.