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Question
Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.
12, 32, 52, 72, ...
Solution
12, 32, 52, 72, ...
Here,
First term (a) = 12
`a_1 = 3^2`
`a_2 = 5^2`
Now, for the given to sequence to be an A.P,
Common difference (d) `= a_1 - a = a_2 - a_1`
Here,
`a_1 - a = 3^2 - 1^2`
= 9 - 1
= 8
Also,
`a_2 - a_1 = 5^2 - 3^2`
= 25 -9
= 16
Since `a_1 - a ≠ a_2 - a_1`
Hence, the given sequence is not an A.P
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