Question

find the sum of two digit odd numbers

Answer 1

it will always be even number

Answer 2

Two digit odd positive numbers are 11,13,15,17...........99 are in A.P.

 Here a = 11 and d = 2, tn= 99, n = ?

Sum of the n terms = (n/2)[2a+(n -1)d]

But tn = a + (n -1)d

⇒ 99 = 11+ (n-1)2

⇒ 99 -11 = (n-1)2

⇒ 88/2 = (n-1)

∴ n = 45.

subsitute n = 45  in sum of the n terms we obtain

⇒ s45 = (45/2)(2×11 + (45 -1)2)

⇒ s45 = (45/2)(110)

⇒ s45 = 45×55.

⇒  s45 = 2475.

∴sum of all two digit odd positive numbers = 2475