Q. 15

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

Answer :

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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