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If the sum of first $n$ terms of an A.P. is given by $S_n = \frac{n}{2}(2n + 8)$. Then, find its first term and common difference. Hence, find its $15^{th}$ term.
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$S_1 = a = 5$ [$\frac{1}{2}$ mark]
$S_2 = 12$ [$\frac{1}{2}$ mark]
Therefore $d = 2$ [$1$ mark]
Hence $a_{15} = 33$ [$1$ mark]
$S_2 = 12$ [$\frac{1}{2}$ mark]
Therefore $d = 2$ [$1$ mark]
Hence $a_{15} = 33$ [$1$ mark]