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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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