Question

Find the sum of all $2$-digit odd positive numbers.

Answer 1

$11,13,15,-------99$

$\therefore a=11,d=2,a_n=99$

$\therefore$ $99=11+(n+1)2$

$88=2(n-1)$

$44+1=n$

$n=45$

$S_n=\frac{n}{2}(a+l)=\frac{45}{2}(11+99)$

$=\frac{45}{2}\times 110$

$=45\times 55$

$=2475$