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

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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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