Question

Without adding, find the sum of the following number

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25

Answer 1

$1+3+5....25$

$a=1$ it's an AP

$d=2$

$25=1+(n-1)2$

$24=(n-1)2$

$n-1=12$

$n=13$

Sum $=\frac{n[a+\ell ]}{2}=\frac{13[1+25]}{2}$

$=13\times 13$

$=169$