Question

Solve the equation - 4 + (- 1 )+ 2 + ............+ X = 437

Answer 1

$ap = \: - 4 + ( - 1) + 2 + .... + x = 437$
$a = - 4 \\ d = 3 \\ s = \frac{n}{2}(2a + (n - 1)d) = 437 \\ = \frac{n}{2} ( - 8 + 3n - 3) = 437 \\ = n( - 11 + 3n) =87 4 \\ = - 11n + {3n }^{2} = 874 \\ = {3n }^{2} - 11n - 874 = 0$
$= (n - 19)(3n + 46)$
therefore
$n = 19$
now to find the last term
$l = a + (n - 1)d \\ - 4 + (19 - 1)3 = 50$
so the answer is 50