Question

find the sum of all 2 digit odd positive numbers

Answer 1

The number will start from 11 and end with 99

and common difference d=2 so the numbers are in AP

Tn = 99 , a = 11 , d=2

Tn = a + (n - 1)d

⇒99 = 11 + (n - 1)2

⇒99-11 = (n - 1)2

⇒88 = 2(n - 1)

⇒44 = n-1

⇒n = 45

Now sum of terms,

sum = n(a + l)/2 where l = 99

sum = 45(11 + 99)/2

= 45 × 110/2

= 45×55

= 2475, so the sum of digits are 2475