# 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 an = 99

We know that,

an = 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

S45 = 2475

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

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