Question

Write the first five terms of each of the following sequences.
$F_1=F_2=1$ and $F_n=F_{n-1}+F_{n-2},n=3,4,.....$

Answer 1

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.