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UPSC NDA I 2017 Mathematics Solved Paper

Question : 27 of 120

Marks: +1, -0

The sum of all the two-digit odd numbers is

Solution:

Concept:

The sum of an arithmetic progression is

S_n = \frac{n}{2}(a + l)

where

a

is the first term,

l

is the last term, and

n

is the number of terms.

Explanation:

Two-digit odd numbers form an arithmetic progression:

11, 13, 15, \dots, 99

Here,

a = 11

d = 2

, and

l = 99

Find

n

using

a_n = a + (n-1)d

99 = 11 + (n-1) \times 2

This gives

88 = (n-1) \times 2

, so

44 = n-1

, hence

n = 45

Now use the sum formula:

S_{45} = \frac{45}{2}(11 + 99) = \frac{45}{2} \times 110 = 45 \times 55 = 2475

Answer:

2475 (Option A)

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