95
(A) Find the sum of the A.P. $7, 10\frac{1}{2}, 14, \dots, 84$.
OR
(B) 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.
OR
(B) 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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(A) $a = 7, d = \frac{21}{2} - 7 = \frac{7}{2}$ [$1$ mark]
$84 = 7 + (n - 1) \times \frac{7}{2} \Rightarrow n = 23$ [$1$ mark]
$S_{23} = \frac{23}{2}(7 + 84) = \frac{2093}{2}$ [$1$ mark]
OR
(B) $S_1 = a = 5$ [$\frac{1}{2}$ mark]
$S_2 = 12$ [$\frac{1}{2}$ mark]
Therefore $d = 2$ [$1$ mark]
Hence $a_{15} = 33$ [$1$ mark]
$84 = 7 + (n - 1) \times \frac{7}{2} \Rightarrow n = 23$ [$1$ mark]
$S_{23} = \frac{23}{2}(7 + 84) = \frac{2093}{2}$ [$1$ mark]
OR
(B) $S_1 = a = 5$ [$\frac{1}{2}$ mark]
$S_2 = 12$ [$\frac{1}{2}$ mark]
Therefore $d = 2$ [$1$ mark]
Hence $a_{15} = 33$ [$1$ mark]