Question:
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
Solution:
We have:
$a_{n}=2 n^{2}+n+1$
$a_{1}=2 \times 1^{2}+1+1$
= 4
$a_{2}=2 \times 2^{2}+2+1$
=11
$a_{3}=2 \times 3^{2}+3+1$
=22
$a_{2}-a_{1}=11-4$
=7
and $a_{3}-a_{2}=22-11$
=11
Since, $a_{2}-a_{1} \neq a_{3}-a_{2}$
Hence, it is not an AP.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.