Answer:
a)
[tex]a_n=3.a_{n-1}[/tex]
[tex]a_1=6[/tex]
b)
[tex]a_n=6(3)^{n-1}[/tex]
Step-by-step explanation:
Recursive And Iterative Rules For Sequences
The recursive rules allow finding terms of a sequence as a function of the previous one. The iterative rules provide a formula to compute the n-th term without the need to compute the previous terms.
Our sequence goes like 6,18,54,162... It can be found that any term equals the previous one by 3
a) The recursive rule can be deducted from the above sentence
[tex]a_n=3.a_{n-1}[/tex]
[tex]a_1=6[/tex]
It's important to provide the first term where the rule will eventually stop
b) The iterative rule is found with the help of geometric sequences
[tex]a_n=a_1r^{n-1}[/tex]
With [tex]a_1=6[/tex] and r=3
[tex]a_n=6(3)^{n-1}[/tex]
