Q. 255.0( 2 Votes )

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

Answer :

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[55]


S45 = 2475


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


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