Q17 of 36 Page 161

If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is

Given: Sn = 3n + 2n2

To find: Common Difference of A.P i.e.‘d’


Consider,


Sn = 3n + 2n2 [given]


Putting n = 1, we get


S1 = 3(1) + 2(1)2


= 3 + 2


S1 = 5


Putting n = 2, we get


S2 = 3(2) + 2(2)2


= 6 + 2(4)


= 6 + 8


S2 = 14


Now, we know that,


S1 = a1


⇒ a1 = 5


and a2 = S2 – S1


= 14 – 5


= 9


∴ Common Difference, d = a2 – a1


= 9 – 5


= 4


Hence, the correct option is (d)

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