Which of the following statements is correct?

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The sum of first n even natural numbers is n².

The sum of first n prime natural numbers is n².

The sum of first n composite natural numbers is n².

The sum of first n odd natural numbers is n².

answer is A.

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Detailed Solution

The sum of first n odd natural numbers is n².

For example,

1 [odd number] = 1 = 1²

1 + 3 [sum of first two odd numbers] = 4 = 2²

1 + 3 + 5 [sum of first three odd numbers] = 9 = 3²

1 + 3 + 5 + 7 [sum of first four odd numbers] = 16 = 4²

∴1 + 3 + 5 + 7 + … + n = n², where n is an odd number.

Thus, statement A is correct.

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