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The set of odd numbers is an arithmetic sequence. Let say that the sequence has n odd numbers where the first term is a1 and the last one is n.

The formula to find the sum on nth terms for an arithmetic sequence is:

Sn = (n/2)(a1 + an) or

Sn = (n/2)[2a1 + (n - 1)d] where d is the common difference that for odd numbers is 2.

Sn = (n/2)(2a1 + 2n - 2)

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Q: What is the formula to find sum of n odd numbers?
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Is sum of odd numbers always even?

The sum of two odd numbers is always even; the sum of three odd numbers is always odd; the sum of four odd numbers is always even; the sum of five odd numbers is always odd; etc


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