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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, 2a, 3a, 4a …
Solution
a, 2a, 3a, 4a …
It can be observed that
a2 − a1 = 2a − a = a
a3 − a2 = 3a − 2a = a
a4 − a3 = 4a − 3a = a
i.e., ak+1 − ak is same every time. Therefore, d = a
The given numbers are in A.P.
Three more terms are
a5 = 4a + a = 5a
a6 = 5a + a = 6a
a7 = 6a + a = 7a
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