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Solve the equation : $-4+(-1)+2 + 5 + ..... + x = 437$.
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$-4+(-1)+2 + 5 + ..... + x = 437$
Here a = $-4$, d = $3$
$-4 + (n - 1)3 = x \Rightarrow n = \frac{x + 7}{3}$
$S_n = 437$
$\Rightarrow \frac{n}{2}(a+x) = 437$
$\Rightarrow \frac{(\frac{x+7}{3})}{2}(-4+x) = 437$
$\frac{(x+7)(x-4)}{6} = 437$
$x^2 + 3x - 28 = 437 \times 6 = 2622$
$x^2 + 3x - 2650 = 0$
$(x + 53)(x - 50) = 0$
$x \ne -53, x = 50$
Here a = $-4$, d = $3$
$-4 + (n - 1)3 = x \Rightarrow n = \frac{x + 7}{3}$
$S_n = 437$
$\Rightarrow \frac{n}{2}(a+x) = 437$
$\Rightarrow \frac{(\frac{x+7}{3})}{2}(-4+x) = 437$
$\frac{(x+7)(x-4)}{6} = 437$
$x^2 + 3x - 28 = 437 \times 6 = 2622$
$x^2 + 3x - 2650 = 0$
$(x + 53)(x - 50) = 0$
$x \ne -53, x = 50$