Question

Show that the sequence defined by a_n = 3n² − 5 is not an A.P

Answer 1

In the given problem, we need to show that the given sequence is not an A.P

Here,

a_n = 3n² − 5

Now, first, we will find its few terms by substituting  n = 1, 2, 3,4,5

so

Substituting n = 1, we get

`a_1 = 3(1)^2 - 5`

`a_1 = -2`

Substituting n = 2, we get

`a_2 = 3(2)^2 - 5`

`a_2 = 7`

Substituting n = 3, we get

`a_3 = 3(3)^2 - 5`

`a_3 = 22`

Substituting n = 4, we get

`a_4 = 3(5)^2 - 5`

`a_4 = 43`

Substituting n = 5, we get

`a_5 = 3(5)^2  - 5`

`a_5 = 70`

Further, for the given sequence to be an A.P,

We find the common difference (d)  = `a_2 - a_1 - a_3 - a_2`

Thus

`a_2 - a_1 = 7 - (-2)`

= 9

Also

`a_3 - a_2 = 22 -7`

= 15

So,`a_2 - a_1 != a_3 - a_2`

Hence, the given sequence is not an A.P.