Question

Show that the sequence defined by
an = 2n^2+n+1 is not in an A.P

Answer 1

Answer:

Step-by-step explanation:

A_n = 2n² + n + 1

Putting n=1,

A_1 = 2 × 1² + 1 + 1= 4

Putting n=2,

A_2 = 2 × 2² + 2 + 1 = 11

Putting n=3,

A_3 = 2 × 3² + 3 + 1 = 22

Common difference of A_2 &A_3 is ( A_3-A_2) = 22 - 11 = 11

Common difference of A_1 & A_2 is ( A_2 - A_1) = 11 - 4 = 7

Clearly, we see that, common difference are not same, so, given sequence A_n is not in an A.P.