If $1, 4, 7, . . .$ are in A.P, then find the common difference and its $n^{t h}$ term.

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Solution

$d = t_{2} - t_{1} = t_{3} - t_{2} = . . .$

$d = 4 - 1 = 7 - 4 = 3$

$t_{n} = a + (n - 1) d$

$t_{n} = 1 + (n - 1) 3$

$t_{n} = 1 + 3 n - 3 = 3 n - 2$

$∴ t_{n} = 3 n - 2$

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