Q. 16 B5.0( 5 Votes )

# Find the sum of a

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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