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

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ConceptArithmetic Progression - Finding Sum of Their First ‘N’ Terms.

#### 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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#### APPEARS IN

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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