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Find the Sum of All Odd Natural Numbers Less than 50 - ICSE Class 10 - Mathematics

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Question

Find the sum of all odd natural numbers less than 50

Solution

Odd natural numbers less than 50 are as follows

1, 3, 5, 7, 9, ........, 49

Now, 3 - 1 = 2, 5 - 3 = 2 and so on

Thus, this forms an A.P. with first term a  = 1, common difference d = 2 and last term l = 49

Now, l = a + (n -1)d

``=> 49 = 1 + (n - 1) xx 2`

` => 48 = (n - 1) xx 2`

`=> 24 = n - 1`

`=> n = 25`

Sum of first n terms = `S = n/2 [a + 1]`

=> Sum of odd natural numbers less than 50 = `25/2 [1 + 49]`

`= 25/2 xx 50`

= 625

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Solution Find the Sum of All Odd Natural Numbers Less than 50 Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms..
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