If f ( 1 ) = 2 f(1)=2 and f ( n ) = 4 f ( n − 1 ) − 2 f(n)=4f(n−1)−2 then find the value of f ( 5 ) f(5).

Answer 1

Plug in values for n

We'll plug in n = 1, 2, 3, 4, and 5

We get the equations:

f(1) = 4f(0) - 2

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

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

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

f(5) = 4f(4) - 2

The second equation says f(2) = 4f(1) - 2

We know what f(1) is, so we can find f(2)

f(2) = 4(2) - 2 = 6

Now, we'll use f(2) to find f(3) in that third equation

Then use f(3) to find f(4) and work your way down