If f(1)=6f(1)=6 and f(n+1)=4f(n)-1f(n+1)=4f(n)−1 then find the value of f(4)f(4).

Answer 1

f(n+1) = 4f(n) - 1

Therefore,

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

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

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

...

So basically you're moving up the stairs here. Use f(1) to find f(2).

f(2) = 4 * (6) - 1 = 23

Then use f(2) to find f(3)

f(3) = 4 * (23) - 1 = 91

Lastly get f(4) using f(3)