Question

The nth term of a sequence is given by 2n ^2 +n +1. Show that it is not an ap

Answer 1

an= 2n^2+n+1
let n 1,2,3,.....
a1= 2(1)^2+1+1= 2+2=4
a2=2(2)^2+2+1=8+3=11
a3=2(3)^2+3+1= 11+4=15
now common difference
a2-a1=a3-a2
11-4=15-11
7≠4
since the common difference is not equal
this is not an ap.