MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

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

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