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4) A sequence is defined recursively by f(1) = 2
and f(n) = 3f(n-1) + 1. Find the first three
terms of the sequence.

- How do I do this question and just Recursive Sequences in general?

4 A sequence is defined recursively by f1 2 and fn 3fn1 1 Find the first three terms of the sequence How do I do this question and just Recursive Sequences in g class=

Respuesta :

r3t40

[tex]S=[2,7,22,\dots][/tex].

Let me explain why.

[tex]f(1)=2[/tex] this is our first term.

[tex]f(2)=3f(2-1)+1=3f(1)+1=7[/tex] second term.

[tex]f(3)=3f(3-1)+1=3f(2)+1=22[/tex] third term.

...

Pretty simple huh?

Hope this helps.

Answer:

The first 3 terms are 2, 7, 22.

Step-by-step explanation:

The n is the sequence number of the term: f(1) means the first term.

The second term

f(2) = 3f(n - 1) + 1   We make n  = 2:

=  3f(2-1) + 1

=  3f(1) + 1        f(1) = 2 so:

=  3*2 + 1

=  7.

3rd term f(3)

= 3f(3 - 1) + 1

= 3f(2) + 1

=  3(7) + 1

= 22.

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