This is A Fibonacci Sequence where the next term is the SUM of the two previous terms:
an = a1 + f × (n-1)
Answer:
The recursive equation for the given sequence is:
[tex]\left \{ {{f_{0} = 6} \atop {{f_{1} = 8} \atop {f_{n} = f_{n-1} + f_{n-2}\hspace{0.5cm}n \geq 2}}} \right.[/tex]
Step-by-step explanation:
Starting with 6 and 8, the next term is the sum of the two previous terms. This is a Fibonacci Sequence with initial values 6 and 8.
We can write the initial values as:
[tex]f_{0} = 6 \\ f_{1} = 8[/tex]
Since the next term of the sequence is the sum of the two previous ones, the recursive step can be stated as follows:
[tex]f_{n} = f_{n-1} + f_{n-2} \hspace{0.8cm}n \geq 2[/tex]
Notice that this step needs the initial values and can only be calculate for values of n equal or greater than 2.
Finally the recursive equation is:
[tex]\left \{ {{f_{0} = 6} \atop {{f_{1} = 8} \atop {f_{n} = f_{n-1} + f_{n-2}\hspace{0.5cm}n \geq 2}}} \right.[/tex]
