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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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