Find the sum of all the two digit odd positive integers.

The two digit odd positive integers are

11, 13, 15,…, 99

a₂ – a₁ = 13 – 11 = 2

a₃ – a₂ = 15 – 13 = 2

∵ a₃ – a₂ = a₂ – a₁ = 2

Therefore, the series is in AP

Here, a = 11, d = 2 and a_n = 99

We know that,

a_n = a + (n – 1)d

⇒ 99 = 11 + (n – 1)2

⇒ 99 – 11 = (n – 1)2

⇒ 88 = (n – 1)2

⇒ 44 = (n – 1)

⇒ n = 45

Now, we have to find the sum of this AP

⇒ S₄₅ = 45[11 + 44]

⇒ S₄₅ = 45[55]

⇒ S₄₅ = 2475

Hence, the sum of all two digit odd numbers are 2475.