Answer:
[tex]a_1=2\\a_n=a_{n-1}+(n-1)\,,n>1[/tex]
Step-by-step explanation:
Given: The smaller branches spiral in the pattern [tex]\{2,3,5,8,...\}[/tex] from a larger limb.
To model: the tree growth with the Fibonacci sequence
Solution:
Take [tex]a_1=2[/tex]
Let [tex]a_n[/tex] denotes the [tex]n^{th}[/tex] term.
[tex]a_2=3=2+1=2+(2-1)=a_1+(2-1)\\a_3=5=3+2=3+(3-1)=a_2+(3-1)\\a_4=8=5+3=5+(4-1)=a_3+(4-1)[/tex]
So,
[tex]a_1=2\\a_n=a_{n-1}+(n-1)\,,n>1[/tex]
Answer:
Yes.
Step-by-step explanation:
The pattern in which the branches are growing off the limb is {1, 1, 2, 3, 5, 8, …}, meaning you can use the model with tree growth.
