If Sn, the sum of first n terms of an AP, is given by
$S_{n}$ = $5 n^{2}$ - 2n, find the common difference of the AP.

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Solution

To find the sum of the first and second terms of the AP.
$S_{n}$ = $5 n^{2}$ - 2n
$S_{1}$ = $5 (1)^{2}$ - 2(1)
$S_{1}$ = 5-2 = 3
$S_{2}$ = 5(2)2 - 2(2)
$S_{2}$ = 20 - 4 = 16

To find the first and second terms of the AP.
$a_{1}$ = $S_{1}$ =3
$a_{2}$ = $S_{2} - S_{1}$ = 16 - 3 = 13

To find the common difference
d = $a_{2}$ - $a_{1}$
d= 13-3 =10

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If Sn, the sum of first n terms of an AP, is given by Sn = 5n2 - 2n, find the common difference of the AP.

To find the sum of the first and second terms of the AP. Sn = 5n2 - 2n S1 = 5(1)2 - 2(1) S1 = 5-2 = 3 S2 = 5(2)2 - 2(2) S2= 20 - 4 = 16 To find the first and second terms of the AP. a1=S1=3 a2 = S2−S1 = 16 - 3 = 13 To find the common difference d = a2-a1 d= 13-3 =10

If Sn, the sum of first n terms of an AP, is given by
$S_{n}$ = $5 n^{2}$ - 2n, find the common difference of the AP.