Question

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

Answer 1

Hence proved. I think it will help you

Answer 2

The sequence defined  by $a_n = 3n^2 - 5$ is not an A.P as common difference is not same.

Step-by-step explanation:

To show : The sequence defined  by $a_n = 3n^2 - 5$ is not an A.P ?

Solution :

In A.P the difference between the consecutive terms is constant.

So, we find the first three terms

Put n=1,

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

$a_1= -2$

Put n=2,

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

$a_2= 7$

Put n=3,

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

$a_3= 22$

The difference between first two terms,

$d_1=a_2-a_1$

$d_1=7-(-2)$

$d_1=9$

The difference between next two terms,

$d_2=a_3-a_2$

$d_2=22-7$

$d_2=15$

As $d_1\neq d_2$

The sequence defined  by $a_n = 3n^2 - 5$ is not an A.P.

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