Function Question

[esthernnassanga]

If n is an integer, f(n) = f(n - 1) - n, and f(4) = 10. What is the value of f(6)?

[sd]

f(6) = f(5) - 6
= f(4) - 5 - 6
= f(4) - 11
= 10 -11
= -1

Whats the OA?

[jenaizhang]

f(n)= F(n-1) - f(n)
f(4)=10

then f(5) = F(4) - f(5) or 2 F(5) = 10 or F(5) = 5

then 2F(6) = 5 amd F(6) = 2.5

[cumic]

jenaizhang has made a new question.

[esledge]

Indeed :-) It makes a difference whether that subtracted term is n or f(n)!

But in any case, I think we are seeing that recursive functions (those in which one term is defined somehow by another term in the sequence) require recursive solutions: f(6) put in terms of f(5), which is then put in terms of f(4), etc. Remember this anytime you see f(n-1) or f(n+1) or f(n-2) in a function/sequence definition.