edenhope edenhope
  • 04-04-2018
  • Mathematics
contestada

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

Respuesta :

wagonbelleville wagonbelleville
  • 08-02-2019

Answer:

f(2) = 3

Step-by-step explanation:

We have that,

The recursive formula of the sequence is [tex]f(n+1)=-f(n)+5[/tex], n> 0.

Also, [tex]f(0)=3[/tex].

Then, the next term is, [tex]f(1)=f(0+1)=-f(0)+5[/tex] i.e. [tex]f(1)=-3+5[/tex] i.e. [tex]f(1)=2[/tex].

Thus, we have,

[tex]f(2)=f(1+1)=-f(1)+5[/tex] i.e. [tex]f(2)=-2+5[/tex] i.e. [tex]f(2)=3[/tex].

Thus, f(2) is 3.

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