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} …

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#### Solution

1^{2}, 3^{2}, 5^{2}, 7^{2} …

Or, 1, 9, 25, 49 …..

It can be observed that

*a*_{2} − *a*_{1} = 9 − 1 = 8

*a*_{3} − *a*_{2 }= 25 − 9 = 16

*a*_{4} − *a*_{3} = 49 − 25 = 24

i.e., *a*_{k}_{+1 }− *a*_{k} is not the same every time.

Therefore, the given numbers are not in A.P.

Concept: Arithmetic Progression

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