Find the first six terms of the sequence given by
$a_{1} = a_{2} = a_{3} = 1$ and $a_{n} = a_{n - 1} + a_{n - 2}$ for $n > 3$

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Solution

The given sequence is $a_{n} = a_{n - 1} + a_{n - 2}$ where the first three terms are $a_{1} = a_{2} = a_{3} = 1$ .

The next three terms of the sequence $a_{n} = a_{n - 1} + a_{n - 2}$ using $a_{1} = a_{2} = a_{3} = 1$ can be determined as follows:

$a_{4} = a_{4 - 1} + a_{4 - 2} = a_{3} + a_{2} = 1 + 1 = 2$

$a_{5} = a_{5 - 1} + a_{5 - 2} = a_{4} + a_{3} = 2 + 1 = 3$

$a_{6} = a_{6 - 1} + a_{6 - 2} = a_{5} + a_{4} = 3 + 2 = 5$

Hence, the first six terms of the sequence $a_{n} = a_{n - 1} + a_{n - 2}$ are $1, 1, 1, 2, 3, 5....$

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