Question

A sequence {tn} is given by tn= n2-1,n €N show that it is not Ap

Answer 1

Answer:

Step-by-step explanation:

Tn=n^2-1

For the sequence to be ap the difference between two consequent terms must be constant

So, Tn+1-Tn=(n+1)^2 -n^2=(n+1-n)(n+1+n)=2n+1

Which changes for every value of n

Thus the sequence Tn is not AP

Answer 2

Given :
tn = n^2 -1
first substitute the value of n = 1
then t1 =2^1-1= 1
t2 = 2^2-1 =3
t3 = 2^3-1 =7
1,3,7 is an A. P
where d1= t2 - t1
= 3 - 1
d1= 2
d2 = t3 -t2
=7- 3
= 4
hence d1 is not equal to d2
hence it is not an A.P