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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:
12, 52, 72, 73 …
Solution
12, 52, 72, 73 …
Or 1, 25, 49, 73 …
It can be observed that
a2 − a1 = 25 − 1 = 24
a3 − a2 = 49 − 25 = 24
a4 − a3 = 73 − 49 = 24
i.e., ak+1 − ak is same every time.
Therefore, the given numbers are in A.P.
And, d = 24
Three more terms are
a5 = 73 + 24 = 97
a6 = 97 + 24 = 121
a7 = 121 + 24 = 145
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