Write the first five terms of the sequence
$a_{1} = 3, a_{n} = 3 a_{n - 1} + 2$ for all $n > 1$

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Solution

$a_{1} = 3$
$a_{n} = {3 a}_{n - 1} + 2$
$\Rightarrow a_{2} = (3 \times 3) + 2 = 11; a_{3} = 3 \times 11 + 2 = 35; a_{4} = 3 \times 35 + 2 = 107$
$a_{5} = 3 \times 107 + 2 = 321 + 2 = 323$

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