Sum

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

1^{2}, 5^{2}, 7^{2}, 73, ...

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#### Solution

1^{2}, 5^{2}, 7^{2}, 73, ...

Here,

First term (*a*) = 1^{2}

a_{1} = 5^{2}

a_{2} = 7^{2}

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 .

Concept: Arithmetic Progression

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