### What is the sum of all two-digit odd positive numbers?

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**Answer: **2475

**Step by Step Explanation: **- We know that smallest two digit odd number is 11, and the greatest two digit number is 99.
- Since difference between consecutive odd numbers is 2, these numbers form an arithmetic progression with first term = 11, last term = 99 and difference = 2.
- If there are total N terms in series, N
^{th} term is given by

T_{N} = T_{1} + (N-1)d

⇒ 99 = 11 + (N-1)(2)

⇒ 2(N - 1) = 99 - 11

⇒ 2(N - 1) = 88

⇒ N - 1 =

⇒ N = 44 + 1

⇒ N = 45
- Now sum of arithmetic progression can be found using standard formula,

S_{N} = ( )[2T_{1} + (N-1)d]

⇒ S_{N} = ( )[2 × 11 + (45-1)(2)]

⇒ S_{N} = ( )[22 + 88]

⇒ S_{N} = ( )[110]

⇒ S_{N} = 45 × 55

⇒ S_{N} = 2475