Question

which of the following can b the nth term of an A.P?
3n+1,2n2+3,n3+n.Give reasons

Answer 1

If A is the first term and D is the common difference of an AP, it's nth term is given by,
Tn = A + (n-1)D = Dn + (A-D).

i.e., the power of n will be always 1.

Thus in the given list only 3n+1 can be the nth term

Answer 2

Answer:

3n +1

Step-by-step explanation:

In case of arithmetic sequence, the difference between two consecutive terms is equal. The general term of A.P. is

$a_n=a+(n-1)d$

We can see that the nth term of A.P represents an equation of straight line. The linear equation is in the form of y = mx +b, here m is slope and b is the y-intercept.

Therefore, we can conclude that nth term of an A.P is a linear function.

Hence, among the given options 3n +1 is linear and hence it represents nth term of an A.P