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I have a sequence {0, 1, 2, 3, 3, 4, 6, 9, 8, ...} for which I am to find the summation of terms to the nth term, Cn

I've broken this down into three alternating sub sequences with the pattern: AP-GP-GP like so {0, 3, 6, ...}, {1, 3, 9, ...} and {2, 4, 8, ...}

To find the sum to the nth term of the bigger sequence it'd just be the sum of the sum to the nth term for each of the sub sequences. Easy enough.

However, the number of terms in the sub sequence, N ≠ n, the number of terms in the larger sequence. I need a way to represent N in terms of n in order to arrive at a single formula for Cn. I've determined that it can be N = n/3 but this is only true for cases where n is a multiple of 3. How do I find those two cases where n isn't a multiple of 3?

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  • $\begingroup$ n/3 + 1, and n/3 + 2 (or n/3 $\pm$ 1) $\endgroup$ – fleablood Oct 31 '15 at 6:08
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N = (n + i)/3 where i = {0, 1, 2}

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