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Question
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
a, a2, a3, a4 …
Solution
a, a2, a3, a4 …
It can be observed that
a2 − a1 = a2 − a = a (a − 1)
a3 − a2 = a3 − a2 = a2 (a − 1)
a4 − a3 = a4 − a3 = a3 (a − 1)
i.e., ak+1 − ak is not the same every time.
Therefore, the given numbers are not in A.P.
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