Question

Which of the following are APs?

If they form an A.P. find the common difference $d$ and write three more terms.

$1^2,3^2,5^2,7^2\dots$

Answer 1

Solution.

The given series $1^2,3^2,5^2,7^2\dots$ can be expressed as $1,9,25,49\dots ..$

The difference between the terms is:

$$\begin{gathered} 9-1=8 \\ 25-9=16 \\ 49-25=24 \end{gathered}$$

Since, the common difference is not same every time. So, the series is not an A.P.

Hence, the given series doesn’t form an A.P.