Sum

If the sum of *n* terms of an A.P. is S_{n} = 3n^{2} + 5n. Write its common difference.

Advertisement Remove all ads

#### 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 *n *in (1) and (2), we get,

dn = 6n

d = 6

Therefore, the common difference is **d = 6** .

Concept: Sum of First n Terms of an AP

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads