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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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