State whether the following sequence is an A.P. or not:
$3, 6, 12, 24, . . . . .$

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Solution

If difference between two consecutive terms are equal, then sequence is called an A.P.
Sequence is $3, 6, 12, 24, . . . .$
Here, $t_{1} = 3, t_{2} = 12, t_{4} = 24$
$t_{2} - t_{1} = 6 - 3 = 3$
$t_{3} - t_{2} = 12 - 6 = 6$
$∴ 3 \neq 6$
$∴ t_{2} - t_{1} \neq t_{3} - t_{2}$
$∴$ Sequence is not an A.P.

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