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In an A.P., it is given that $a = 2, d = 8$ and $S_n = 90$. Find the value of $n$.
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Solution: (a) $S_n = \frac{n}{2}[2a + (n - 1)d] = 90$ (1 Mark)
$\frac{n}{2}[4 + (n - 1)8] = 90 \Rightarrow n[2 + 4n - 4] = 90 \Rightarrow n[4n - 2] = 90 \Rightarrow 4n^2 - 2n - 90 = 0 \Rightarrow 2n^2 - n - 45 = 0$ (1 Mark)
$\Rightarrow (2n+9)(n-5) = 0 \Rightarrow n = 5, -\frac{9}{2}$ (rejected) (
frac{1}{2} Mark)
$\Rightarrow n = 5$ (
frac{1}{2} Mark)
$\frac{n}{2}[4 + (n - 1)8] = 90 \Rightarrow n[2 + 4n - 4] = 90 \Rightarrow n[4n - 2] = 90 \Rightarrow 4n^2 - 2n - 90 = 0 \Rightarrow 2n^2 - n - 45 = 0$ (1 Mark)
$\Rightarrow (2n+9)(n-5) = 0 \Rightarrow n = 5, -\frac{9}{2}$ (rejected) (
frac{1}{2} Mark)
$\Rightarrow n = 5$ (
frac{1}{2} Mark)