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# Find the Sum of All Odd Numbers Between 100 and 200. - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Question

Find the sum of all odd numbers between 100 and 200.

#### Solution

In this problem, we need to find the sum of all odd numbers lying between 100 and 200.

So, we know that the first odd number after 0 is 101 and the last odd number before 200 is 199.

Also, all these terms will form an A.P. with the common difference of 2.

So here,

First term (a) = 101

Last term (l) = 199

Common difference (d) = 2

So, here the first step is to find the total number of terms. Let us take the number of terms as n.

Now, as we know,

a_n = a + (n - 1)d

So, for the last term,

199 = 101 + (n - 1)2

199 = 101 + 2n - 2

199 = 99 + 2n

199 - 99 = 2n

Further simplifying,

100 = 2n

n = 100/2

n = 50

Now, using the formula for the sum of n terms,

S_n = n/2 [2a + (n -1)d]

For n = 50 we get

S_n = 50/2 [2(101) + (50 - 1)2]

= 25 [202 + (49)2]

= 25(202 + 98)

= 25(300)

= 7500

Therefore the sum of all the odd numbers lying between 100 and 200 is S_n = 7500

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Solution Find the Sum of All Odd Numbers Between 100 and 200. Concept: Sum of First n Terms of an AP.
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