Respuesta :
Answer:
[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]
Step-by-step explanation:
Recursive means you want to define a sequence in terms of other terms of your sequence.
The common ratio is what term divided by previous term equals.
The common ratio here is -6/2=18/-6=-54/18=-3.
Or in terms of the nth and previous term we could say:
[tex]\frac{a_n}{a_{n-1}}=r[/tex]
where r is -3
[tex]\frac{a_n}{a_{n-1}}=-3[/tex]
Multiply both sides by the a_(n-1).
[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]
Answer:
see explanation
Step-by-step explanation:
A recursive rule allows us to obtain any term in the sequence from the previous term.
These are the terms of a geometric sequence with common ratio r
r = - 6 ÷ 2 = 18 ÷ - 6 = - 54 ÷ 18 = - 3
Thus to obtain a term in the sequence multiply the previous term by - 3
[tex]a_{n+1}[/tex] = - 3 [tex]a_{n}[/tex] with a₁ = 2
