What is "if f(1) = 160 and f(n + 1) = –2f(n)?

The given function relationship f(n + 1) = –2f(n) is a recursive formula that defines the function f(n) in terms of its previous value f(n-1).

If we are given that f(1) = 160, we can use the recursive formula to calculate the values of f(n) for other values of n.

• f(2) = -2f(1) = -2160 = -320
• f(3) = -2f(2) = -2(-320) = 640
• f(4) = -2f(3) = -2640 = -1280
• f(5) = -2f(4) = -2(-1280) = 2560

And so on.

The function f(n) will alternate between positive and negative values, following the pattern of multiplication by -2 at each step. The values will increase or decrease rapidly as n grows larger.