Question

Which of the following are APs? If they form an A.P. find the common difference $d$ and write three more terms.

$1^2,5^2,7^2,73\dots$

Answer 1

Arithmetic Progression:

The given series $1^2,5^2,7^2,73\dots$ can be expressed as $1,25,49,73\dots$

The difference between each term is,

$$\begin{gathered} 25-1=24 \\ 49-25=24 \\ 73-49=24 \end{gathered}$$

Since, the common difference is same every time.

Therefore, $d=24$ and the given series forms an A.P.

Thus, the next three terms are;

$$\begin{gathered} 73+24=97 \\ 97+24=121 \\ 121+24=145 \end{gathered}$$

Hence, the given series is an A.P. and the common difference is $d=24$ and the next three terms are$97,121,145$.