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If the sum of first $6$ terms of an A.P. is $36$ and that of the first $16$ terms is $256$, find the sum of first $10$ terms.
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$S_6 = 36 \Rightarrow \frac{6}{2}[2a + 5d] = 36$
$2a + 5d = 12$ ----- (1)
$S_{16} = 256 \Rightarrow \frac{16}{2}[2a + 15d] = 256$
$2a +15d = 32$ ----- (2)
Solving (1) and (2)
$d = 2$
$a = 1$
$S_{10} = \frac{10}{2}[2(1) +9(2)]$
$= 100$
$2a + 5d = 12$ ----- (1)
$S_{16} = 256 \Rightarrow \frac{16}{2}[2a + 15d] = 256$
$2a +15d = 32$ ----- (2)
Solving (1) and (2)
$d = 2$
$a = 1$
$S_{10} = \frac{10}{2}[2(1) +9(2)]$
$= 100$