Question

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

1², 5², 7², 73, ...

Answer 1

1², 5², 7², 73, ...

Here,

First term (a) = 1²

a₁ = 5²

a₂ = 7²

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

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

Here,

`a_2 -a_1 = 5^2 - 1^2`

               = 25 - 1

               = 24

Also,

\[a_3 - a_2 = 7^2 - 5^2 = 49 - 25 = 24\]

Since   `a_1 - a = a_2 - a_1`

Hence, the given sequence is an A.P with the common difference  d = 24 .