If f(1)=1 and f(n+1) = f(n)2 -3 then find the value of f(4)

Question

If f(1)=1 and f(n+1) = f(n)² -3 then find the value of f(4)

Answer 1

f(1) = 1

f(2) = f(1)² - 3 = 1² - 3 = -2

f(3) = f(2)² - 3 = (-2)² - 3 = 4 - 3 = 1

f(4) = f(3)² - 3 = _____?

Looks like this sequence alternates between two values, f(n) = 1 for odd values of n and f(n) = -2 for even values of n.

Answer 2

Given f(1)=1

f(n+1)=f(n)^2-3

Substitute n=1

f(1+1)=f(1)^2-3

f(2)= (1)^2-3

f(2)=1-3

f(2) = -2

You can find out f(3) if you substitute n=2 in the equation.

f(2+1)= f(2)^2-3

f(3) =(-2)^2 -3

f(3) = 4-3

f(3) =1

Same way you can find out f(4). put n=3 in the equation.

f(3+1)= f(3)^2-3

f(4) = (1)^2-3

f(4) = 1-3

f(4) = -2

Answer: f(4)=-2