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# If the Sum of N Terms of an A.P. is Sn = 3n2 + 5n. Write Its Common Difference. - Mathematics

Sum

If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.

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#### Solution

Here, we are given,

S_n = 3n^2 + 5n

Let us take the first term as a and the common difference as d.

Now, as we know,

a_n = S_n - S_(n-1)

So, we get,

a_n = (3n^^^^2 + 5n) - [3(n-1)^2 + 5 (n-1)]

=3n^2 + 5n - [3(n^2 + 1 - 2n) + 5n - 5]      [\text{ Using}  (a - b)^2= a^2 - ab]

=3n^2 + 5n - (3n^2 + 3 - 6n + 5n - 5)

=3n^2 + 5n - 3n^2 - 3 + 6n - 5n + 5

= 6n + 2                             ..................(1)

Also,

a_n = a + (n-1)d

= a + nd - d

= nd + ( a- d)                     ...............(2)

On comparing the terms containing in (1) and (2), we get,

dn = 6n

d = 6

Therefore, the common difference is d = 6 .

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Q 10 | Page 56
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