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Find the sum of all 2 digit odd positive numbers

Posted by Gungun .. 4 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 4 years, 8 months ago

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.

1Thank You

ANSWER

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