Question

Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.

1², 3², 5², 7², ...

Answer 1

1², 3², 5², 7², ...

Here,

First term (a) = 1²

`a_1 = 3^2`

`a_2 = 5^2`

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

Common difference (d)  `= a_1 - a = a_2 - a_1`

Here,

`a_1 - a = 3^2 - 1^2`

             = 9 - 1

             = 8

Also,

`a_2 - a_1 = 5^2 - 3^2`

               = 25 -9 

               = 16

Since  `a_1 - a ≠ a_2 - a_1`

Hence, the given sequence is not an A.P