Question

the common difference of the AP whose general term is an=2n+1


a)1
b)2
c)-1
d)-2

Answer 1

2.

Step-by-step explanation:

an=2n+1

A1=2+1=3

A2=4+1=5

A3=6+1=7

common difference (d)=7-5=2.

Answer 2

Note:

A.P. stands for Arithmetic Progression.

This is a sequence in which the difference between the consecutive terms is same.

Also;

The common difference of an A.P. is given by , d = T(n) - T(n-1)

OR , d = a(n) - a(n-1)

Here,

a(n) = 2n + 1

Thus,

a(n-1) = 2(n-1) + 1

= 2n - 2 + 1

= 2n - 1

Now,

The common difference will be ;

=> d = a(n) - a(n-1)

=> d = (2n+1) - (2n-1)

=> d = 2n + 1 - 2n + 1

=> d = 2

Hence,

The required common difference of the A.P. is 2.

Hence,

Required answer is : option (b)