Idon't know anything about this and obviously i suck at this lol

An arithmetic sequence is a sequence that starts with some term , and the next term is generated by adding a constant to get the second term . Then the next term is generated by adding to , and so on.

Here and . So recursively, the sequence is defined by



is the sum of the first terms of the sequence. Before you can find this sum, an explicit formula for the would be useful. You have




and so on, up to

(Notice there's a pattern on the right hand side between the subscripted term and the coefficient of . They always add up to .)

So the explicit formula for this sequence is



You're asked to find the sum of the first 15 terms, which means



Now you could just find the first 9 terms and add them together, but that's more work than necessary. Instead, you have



There are some well known formulas for the sums of powers:




So you get





The answer is C.