Question

The sum of n terms of an AP is given by Sn= (2n2+3n). What is the common difference of the AP? (a) 3 (b) 4 (c) 5 (d) 9

Answer 1

EXPLANATION

• GIVEN

Sum of an Ap = 2n^2 + 3n

TO FIND COMMON DIFFERENCE.

equation = Sn = 2n^2 + 3n

Tn = Sn - S(n - 1)

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

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

2n^2 + 3n - [2n^2 + 2 - 4n + 3n - 3 ]

2n^2 + 3n - 2n^2 - 2 + 4n - 3n + 3

4n - 2 + 3

4n + 1 = Tn

let we can assume the value of n

CASE = 1

put n = 1

we get,

4(1) + 1 = 5

CASE = 2

put n = 2

we get,

4(2) + 1 = 9

CASE = 3

put n = 3

we get,

4(3) + 1 = 13

CASE = 4

Put n = 4

we get,

4(4) + 1 = 17

series can be written as = 5,9,13,17.....

First term = a = 5

common difference = b - a = d

9 - 5 = 4

Hence,

option [ B ] is correct

VERIFICATION.

a = 5

d = 4

An = a + ( n - 1 ) d

An = 5 + ( n - 1 ) 4

An = 5 + 4n - 4

An = 4n + 1

HENCE VERIFIED