if a sequence is defined recursively by f(0 ) = 3 and f(n+1) = -f(n)+5 for n is equal to or greater than 0, then f(2) is equal to?

if f(n+1)= -f(n) +5
then f(2)=-f(1)+5
we don't know f(1) yet. Use the same rule as above:
f(1)=-f(0)+5, we do know that f(0)=3, so f(1)=-3+5=2
so f(2)=-f(1)+5=-2+5=3

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OrethaWilkison OrethaWilkison · Answer 2 · 2019-03-22T18:02:48+01:00

Answer:

value of f(2) is, 3

Step-by-step explanation:

As per the statement::

[tex]f(0) = 3[/tex]

and recursive formula is given as:

[tex]f(n+1) = -f(n)+5[/tex] .....[1] [tex]n\geq 0[/tex]

To find the value of f(2):

Substitute n = 0 in [1] we have;

[tex]f(1) = -f(0)+5[/tex]

⇒[tex]f(1) = -3+5 = 2[/tex]

⇒[tex]f(1) = 2[/tex]

Now. substitute n =1 we have;

[tex]f(2) = -f(1)+5[/tex]

⇒[tex]f(2) = -2+5 = 3[/tex]

⇒[tex]f(2) = 3[/tex]

Therefore, the value of f(2) is, 3