Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.
$ 3,6,12,24, \ldots . $
Given:
Given sequence is \( 3,6,12,24, \ldots . \)
To do:
We have to find if the given sequence is an A.P. We also have to find the common difference if it is an A.P.
Solution:
A given sequence is in A.P. if the difference between any two consecutive terms is equal.
Here,
$a_1=3, a_2=6, a_3=12, a_4=24$
Therefore,
$a_2-a_1=6-3=3$
$a_3-a_2=12-6=6$
$a_2-a_1≠a_3-a_2$
Hence, the given sequence is not an A.P.
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