# Sum of terms of Arithmetic sequence

Find SUM_(k=10)^15 tk for an arithmetic sequence with 10th term being -10 and 20th term being 15, where tk represents the kth term of this arithmetic sequence.

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#### Solution Preview

If we consider a as the first term of the given arithmetic sequence, and d as the common difference, then kth term will be obtained by adding (k-1) differences to the first term, i.e.

tk = a + (k-1)d

Thus, we can generate following equations.

t10 = a + (10-1)d = ...

#### Solution Summary

Solution shows two different approaches to compute the required sum.

$2.19