if f(1) =1 and f(n) =3f(n-1)then what is f(6)

Answer 1

f(1) = 1

f(2) = 3·f(1) = 3·1 = 3

f(3) = 3·f(2) = 3·3 = 9

f(4) = 3·f(3) = 3·9 = 27

f(5) = 3·f(4) = 3·27 = 81

f(6) = ___?

Answer 2

You might run into a scenario like this if you take a programming class and have to learn recursion. That's where the equation is defined by a previous (for instance) value of the same equation. You have to work your way back to a place where the equation has a known solution, and substitute that known solution, then work your way forward.

Start with n = 6 and work your way back.

f(6) = 3f(5)

f(5) = 3f(4)

f(4) = 3f(3)

f(3) = 3f(2)

f(2) = 3f(1) and since f(1) = 1, you use that knowledge to work your way forward...

f(2) = 3

f(3) = 9

f(4) = 27

f(5) = 81

f(6) = 243 ...and there you go.