Q. 16 B5.0( 5 Votes )

Find the sum of all two-digit odd positive numbers.

Answer :

All the two-digit odd positive numbers are –


11,13,15,17,……….,99


The above series of numbers forms an arithmetic progression with


first term(a) = 11 and,


common difference(d) = (n + 1)th term – nth term = 13 – 11 = 2


last term or nth term(an) = 99


Let the total no. of terms in above A.P be n.


an = a + (n – 1) × d


99 = 11 + (n – 1) × 2


88 = 2n – 2


2n = 90


n = 45


Sum of all the 45 terms of the AP is given by –


S45 =(45/2)(11 + 99)


[Sn = (n/2)(a + l) =(n/2)[(2a + (n – 1)d]


=(45/2) × 110


=45 × 55


=2475


Thus, the sum of all two-digit odd positive numbers = 2475.


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