Question

PLEASE HELP 20 POINTS

Answer 1

Answer:

a)

$a_n=3.a_{n-1}$

$a_1=6$

b)

$a_n=6(3)^{n-1}$

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

$a_n=3.a_{n-1}$

$a_1=6$

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

$a_n=a_1r^{n-1}$

With $a_1=6$ and r=3

$a_n=6(3)^{n-1}$