Is the given sequence 0.2, 0.22, 0.222, 0.2222.... an A.P.?

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Solution

Given sequence is $0.2, 0.22, 0.222, 0.2222, . . . . . . .$
We know that, for a sequence to be an $A . P .$ , the difference between any consecutive terms must be equal.
Here,
$0.22 - 0.2 = 0.02$
$0.222 - 0.22 = 0.002$
$0.2222 - 0.222 = 0.0002$

Since the difference between two consecutive terms is not equal, the given sequence is not an $A . P .$

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