Question

Find the sum of all two-digit odd positive numbers.

Answer 1

All two-digit odd positive numbers are 11, 13, 15, 17, ...., 99. which are in AP with $a=11,d=2,l=99$

Let the number of terms be $n$.

$a_n=99$

$a+(n-1)d=99$

$11+(n-1)\times 2=99$

$n=45$

Sum of n terms is given by

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

$S_n=\frac{45}{2}(11+99)=2475$

Therefore, the sum of all two-digit odd positive numbers is 2475.