The sum of all the odd numbers lying between 100 and 200 is,

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7000

7200

7500

7020

answer is C.

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Detailed Solution

We need to find the sum of all the odd numbers lying between 100 and 200.
The sum of the arithmetic progression is given as,

S n = n 2 2 a + n − 1 d .

where,
The number of terms is n.
The first term is a.
The common difference is d.
Now,
Substitute 101 for

a 1

and 103 for

a 2

d = a 2 − a 1

d = a 2 − a 1 ⇒ d = 103 − 101 ⇒ d = 2

According to the question,

a n = a + n − 1 d ⇒ 199 = 101 + n − 1 2 ⇒ 98 = n − 1 2

⇒ 2 n − 2 = 98 ⇒ 2 n = 100 ⇒ n = 50

Therefore, the sum will be,

S 50 = 502 2101 + 50 − 1 2 ⇒ S 50 = 25 202 + 492 ⇒ S 50 = 25 202 + 98

⇒ S 50 = 25300 ⇒ S 50 = 7500

The sum of all odd numbers lying between 100 and 200 is 7500.
Hence, option 3 is correct.

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