Question

Find without adding: $1+3+5+7+9+11+13+15+17+19+21$

Answer 1

The sum of an Arithmetic progression = 121,
Let the first number be 1 as it is the smallest odd number.
Then, common difference = 2
Sum of an arithmetic progression = $\frac{n}{2}\times (2a+(n-1)d)$ = 121
$\frac{n}{2}\times (2\times 1+(n-1)\times 2)$ = 121
$\frac{n}{2}\times 2n=121$
$n^2=121$
Thus n=11
The series will be, 1,3,5,7,9,11,13,15,17,19,21