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nth Term of A.P

Find the sum ...

Question

Find the sum of all odd natural numbers less than $50$ .

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Solution

S=sum of odd natural numbers less than 50
$= 1 + 3 + 5 + . . . . . . + 49 = (2 (1) - 1) + (2 (2) - 1) + . . . . + (2 (25) - 1) = 2 (1 + 2 + . . . . + 25) - 25 = 25 (25 + 1) - 25 S = 625$

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