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Which of the following represents a recursive sequence?

A.
a(n)=3(n)-2
B.
a(n)=3x3^(n-1)
C.
a(n)=3xa(n-1)
D.
a(n)=3

Answer :

Answer:

Option C is correct.

[tex]a_n=3 a_{n-1}[/tex]

Step-by-step explanation:

For a sequence [tex]a_1, a_2, a_3, . . . , a_n, . . .[/tex]

A recursive formula is a formula that requires the computation of all previous terms in order to find the value of [tex]a_n[/tex]

There is two simple examples of recursive definitions are for:

Arithmetic sequences and geometric sequences.

An arithmetic sequence has a common difference(d) or a constant difference  between each term.

Then the recursive formula for arithmetic sequence is:

[tex]a_n = a_{n-1}+d[/tex]

Next,

for geometric sequence has a common ratio(r)

the recursive formula is given by;

[tex]a_n = ra_{n-1}[/tex]

Therefore, from the given options you can see that the only option C which represents the recursive sequence is, [tex]a_n=3 a_{n-1}[/tex] where r =3 is the common ratio.


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