The given sequence is the sum of two arithmetic sequences, 3n terms of
the first sequence and n terms of the second sequence:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + ... + 3nth term
-10 - 22 - 34 - 46 - ... - nth term
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1 + 3 - 5 + 7 + 9 - 11 + 13 + 15 - 17 + 19 + 21 - 23 + ... ?
The first sequence has 3n terms, but first we find the sum of n terms
and since it has 3n terms, we replace n by 3n and get the sum of 3n terms,
or
The second sequence -10-22-34-46- ... has only n terms:
Adding the two sums:
Answer:
Edwin
