Let a sequence be defined by $a_{1} = 3, a_{n} = {3 a}_{n - 1} + 1$ for all n > 1. Find the first four terms of the sequence.

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Solution

$a_{1} = 3$
$a_{n} = 3 a_{n - 1} + 1$
$a_{2} = 3 a_{1} + 1$
$= 3 (3) + 1 = 10$
$a_{3} = 3 a_{2} + 1$
$= 3 (10) + 1 = 31$
$a_{4} = 3 a_{3} + 1$
$= 3 (31) + 1 = 94$
$3, 10, 31, 94$ .

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Similar questions

Find the first four terms of the sequence defined by $a_{1} = 3$ and $a_{n} = 3 a_{n - 1} + 2$ , for all n > 1.

a_{1} = 3, a_{n} = 3 a_{n - 1} + 2

n > 1

a_{1} = 3, a_{n} = 3 a_{n - 1} + 2

n > 1

a_{n} = 3 a_{n - 1} - a_{n - 2}

n > 2

a_{5}

a_{1} = 4

a_{2} = 3

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