A sequence is defined by the recursive function f(n + 1) = f(n). If f(3) = 9 , what is f(1)?

Solution:

Given recursive function is f(n + 1) = f(n) --- (1)

Step-1:

If n = 1 in (1) then f(1 + 1) = f(1)

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

Step-2:

If n = 2 in (1) then f(2 + 1) = f(2)

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

Step-3:

But f(2) = f(1)

⇒ f(1) = f(3)

But given f(3) = 9

⇒ f(1) = 9

A sequence is defined by the recursive function f(n + 1) = f(n). If f(3) = 9 , what is f(1)?

Summary:

If a sequence is defined by the recursive function f(n + 1) = f(n). If f(3) = 9 ,then f(1) = 9.