Answer:
The recursive rule for the sequence is
[tex]a_{1}[/tex] = x
[tex]a_{2}[/tex] = x
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + [tex]a_{n-2}[/tex]
Step-by-step explanation:
∵ The first term is x
∴ [tex]a_{1}[/tex] = x
∵ The second term is x
∴ [tex]a_{2}[/tex] = x
∵ The third term is 2x
- That means the third term is the sum of the 1st and 2nd terms
∴ [tex]a_{3}[/tex] = [tex]a_{1}[/tex] + [tex]a_{2}[/tex]
∵ The fourth term is 3x
∴ [tex]a_{4}[/tex] = [tex]a_{2}[/tex] + [tex]a_{3}[/tex]
∵ The fifth term is 5x
∴ [tex]a_{5}[/tex] = [tex]a_{3}[/tex] + [tex]a_{4}[/tex]
∵ The sixth term is 8x
∴ [tex]a_{6}[/tex] = [tex]a_{4}[/tex] + [tex]a_{5}[/tex]
From all above the sequence is Fibonacci sequence where its recursive rule is
[tex]a_{1}[/tex] = first term
[tex]a_{2}[/tex] = second term
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + [tex]a_{n-2}[/tex]
The recursive rule for the sequence is
[tex]a_{1}[/tex] = x
[tex]a_{2}[/tex] = x
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + [tex]a_{n-2}[/tex]
