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# Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. (xiv) 1^2, 3^2, 5^2, 7^2,...

Q : 4         Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.

(xiv)  $\small 1^2,3^2,5^2,7^2,...$

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Given series is
$\small 1^2,3^2,5^2,7^2,...$
we can rewrite it as
$1,9,25,49,....$
Now,
the first term to this series is = 1
Now,
$a_1 =1 \ \ and \ \ a_2 = 9 \ \ and \ \ a_3 =25 \ \ and \ \ a_4 = 49$
$a_2-a_1 = 9-1 = 8$
$a_3-a_2 = 25-9=16$
We can clearly see that the difference between terms are not equal
Hence, given series is not in AP

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