Write the first five terms of each of the following sequences.
$F_{1} = F_{2} = 1$ and $F_{n} = F_{n - 1} + F_{n - 2}, n = 3, 4, . . . . .$

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Solution

We are given that $F_{1} = F_{2} = 1$ and $F_{n} = F_{n - 1} + F_{n - 2}$
We can observe that a term is the sum of previous two terms.
Since we are given first two terms all other terms can calculated.
$F_{3} = F_{2} + F_{1} = 1 + 1 = 2$
$F_{4} = F_{3} + F_{2} = 2 + 1 = 3$
$F_{5} = F_{4} + F_{3} = 3 + 2 = 5$

Therefore the first five terms of the series are $1, 1, 2, 3, 5$
This series is called Fibonacci series.

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