Check whether the following sequence is an AP or not:
$3 m - 1, 3 m - 3, 3 m - 5, . . . .$

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Solution

Given, $3 m - 1, 3 m - 3, 3 m - 5, . . . . .$
Here $t_{1} = 3 m - 1, t_{2} = 3 m - 3, t_{3} = 3 m - 5, . . . .$
$∴ t_{2} - t_{1} = (3 m - 3) - (3 m - 1) = - 2$
Also, $t_{3} - t_{2} = (3 m - 5) - (3 m - 3) = - 2$
Hence, the given sequence is an A.P. with first term $3 m - 1$ and the common difference $- 2$ .

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