Question

the nth term of an ap cannot be n^2+n+1,state true or false. justify your answer

Answer 1

nth term = a + (n - 1)d
= a + nd - d
= A + Bn

this is a one degree equation and it can never be a second degree equation in n.

so the answer is false

Answer 2

AP mean a sequence in which difference between two term is always constant
here n^2+n+1
put n=1 t1=3
n=2 t2=7
n=3 t3=13
now we look difference is not constant so this is not in AP