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

Question

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

Answer 1

Since the function is defined recursively, a recursive solution is appropriate.

 

 

f(2) = -f(1) + 5                          [for n=1; recursive case]

f(2) = -( -f(0) + 5 ) + 5             [expand for n=0; recursive case]

f(2) = -( -3 + 5 ) + 5                [given f(0)=3; base case]

f(2) = -(2) + 5

f(2) = 3

Answer 2

f(0 + 1) = -f(0) + 5

f(1) = -3 + 5

f(1) = 2

 

f(1 + 1) = -f(1) + 5

f(2) = -2 + 5

f(2) = 3