Question

Without adding, find the sum of given numbers:

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

Answer 1

This is an arithmetic progression whose first term is 1 and the common difference is 2 and number of terms = 12
Sum of an arithmetic progression = $\frac{n}{2}\times (2a+(n-1)d)$
Therefore, Sum = $\frac{12}{2}\times (2\times 1+(12-1)\times 2)$
Sum = $\frac{12}{2}\times 24$
Sum = $144$