If the sum of first 8 and 19 terms of an A.P. are 64 and 361 respectively, find the common difference.

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Solution

$S_{8} = 64$
$S_{n} = \frac{n}{2} (2 a + (n - 1) d)$
$2 a + 7 d = 16$
$S_{19} = 361$
$2 a + 18 d = 38$
Solving, $a = 1, d = 2$

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If the sum of first 8 and 19 terms of an A.P. are 64 and 361 respectively, find the common difference.

S8=64Sn=n2(2a+(n−1)d)2a+7d=16S19=3612a+18d=38Solving, a=1,d=2

$S_{8} = 64$
$S_{n} = \frac{n}{2} (2 a + (n - 1) d)$
$2 a + 7 d = 16$
$S_{19} = 361$
$2 a + 18 d = 38$
Solving, $a = 1, d = 2$