Question

How many terms of the sequence 13, 10,7............ should be taken so that their sum is 0?

Answer 1

$a = 13. \: \: \: d = 10 - 13 = - 3 \\ \frac{n}{2} (2 \times 13 + (n - 1) \times - 3) = 0 \\ 26 - 3n + 3 = 0 \\ 3n = 29 \\ n = \frac{29}{3} \: not \: an \: integer \\ so \: sum \: cannot \: be \: zero$