Q. 175.0( 3 Votes )

# If the sum of n terms of an A.P. is given by S_{n} = 3n + 2n^{2}, then the common difference of the A.P. is

A. 3

B. 2

C. 6

D. 4

Answer :

Given: S_{n} = 3n + 2n^{2}

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

Consider,

S_{n} = 3n + 2n^{2} [given]

Putting n = 1, we get

S_{1} = 3(1) + 2(1)^{2}

= 3 + 2

S_{1} = 5

Putting n = 2, we get

S_{2} = 3(2) + 2(2)^{2}

= 6 + 2(4)

= 6 + 8

S_{2} = 14

Now, we know that,

**S _{1} = a_{1}**

⇒ a_{1} = 5

and a_{2} = S_{2} – S_{1}

= 14 – 5

= 9

∴ Common Difference, d = a_{2} – a_{1}

= 9 – 5

= 4

Hence, the correct option is **(d)**

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