$1^{2}, 3^{2}, 5^{2}, 7^{2}, \ldots$ are $APs$? If they form an $AP,$ find the common difference $d$ and write three more terms.

(N/A) The given sequence is $1^{2}, 3^{2}, 5^{2}, 7^{2}, \ldots$
This can be written as $1, 9, 25, 49, \ldots$
To check if the sequence forms an $AP$,we calculate the difference between consecutive terms:
$a_{2} - a_{1} = 9 - 1 = 8$
$a_{3} - a_{2} = 25 - 9 = 16$
$a_{4} - a_{3} = 49 - 25 = 24$
Since the difference $a_{k+1} - a_{k}$ is not constant (i.e.,$8 \neq 16 \neq 24$),the given sequence does not form an $AP$.