Question

If the sum of first nterms of an A.P. is given by Sn=2n²+n, then find it's common difference.

Answer 1

EXPLANATION.

• GIVEN

Sum of first n terms of an Ap = Sn = 2n^2 + n

TO FIND IT'S COMMON DIFFERENCE.

Tn = Sn - Sn-1

replace n = ( n - 1)

we get,

Tn = 2n^2 + n - [ 2 ( n - 1)^2 + ( n - 1 )]

2n^2 + n - [ 2 ( n^2 + 1 - 2n ) + n - 1 ]

2n^2 + n - [ 2n^2 + 2 - 4n + n - 1 ]

2n^2 + n - [ 2n^2 - 3n + 1 ]

2n^2 + n - 2n^2 + 3n - 1

4n - 1

put the value of n in equation

we get,

put n = 1

4(1) - 1 = 3

put n = 2

4(2) - 1 = 7

put n = 3

4(3) - 1 = 11

put n = 4

4(4) - 1 = 15

now, series can be written as,

3,7,11,15......

Let first term = a = 3

common difference = d = b - a = 7 - 3 = 4