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If the sum of first $7$ terms of an A.P. is $49$ and that of first $17$ terms is $289$, find the sum of its first $20$ terms.
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Let $a$ be the first term and $d$ be the common difference.
$\frac{7}{2}(2a + 6d) = 49$
$a+3d=7 \dots (i)$
$\frac{17}{2}(2a + 16d) = 289$
$a + 8d = 17 \dots (ii)$
solving (i) and (ii)
$d=2 \& a=1$
$S_{20} = \frac{20}{2} [2(1)+19(2)]$
$= 400$
$\frac{7}{2}(2a + 6d) = 49$
$a+3d=7 \dots (i)$
$\frac{17}{2}(2a + 16d) = 289$
$a + 8d = 17 \dots (ii)$
solving (i) and (ii)
$d=2 \& a=1$
$S_{20} = \frac{20}{2} [2(1)+19(2)]$
$= 400$