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)  ${\displaystyle =a_1-a=a_2-a_1}$

Here,

${\displaystyle a_2-a_1=5^2-1^2}$

               = 25 - 1

               = 24

Also,

$$a_3-a_2=7^2-5^2=49-25=24$$

Since   ${\displaystyle a_1-a=a_2-a_1}$

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