Q. 15

# The nth term of a sequence is given by an = 2n2 + n+ 1. Show that it is not an A.P.

Given,

an = 2n2 + n + 1

We can find first three terms of this sequence by putting values of n from 1 to 3.

When n = 1:

a1 = 2(1)2 + 1 + 1

a1 = 2(1) + 2

a1 = 2 + 2

a1 = 4

When n = 2:

a2 = 2(2)2 + 2 + 1

a2 = 2(4) + 3

a2 = 8 + 3

a2 = 11

When n = 3:

a3 = 2(3)2 + 3 + 1

a3 = 2(9) + 4

a3 = 18 + 4

a3 = 22

First three terms of the sequence are 4, 11, 22.

A.P is known for Arithmetic Progression whose common difference = an – an-1 where n > 0

a1 = 4, a2 = 11, a3 = 22

Now, a2 – a1 = 11 – 4 = 7

a3 – a2 = 22 – 11 = 11

As a2 – a1 is not equal to a3 – a2

The given sequence is not an A.P.

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