A sequence is defined by the recursive function f (n + 1) = f (n) - 2. If f (1) = 10, what is f (3) ?

6

Step-by-step explanation:

Lets see what f (2) is.

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

We are going to replace n with 1 to get f (2):

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

f (2) = f (1) - 2

Since f (1) = 10 we can rewrite as:

f (2) = 10-2

f (2) = 8

We want to find f (3) so now we will replace n with 2:

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

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

f (3) = f (2) - 2

f (3) = 8-2

f (3) = 6.

So f (3) is 6.

Another way:

f (n + 1) = f (n) - 2 says you can find the next term by taking previous and minus 2 from it.

So if we start with first term, f (1), is 10.

Then second term, f (2), is 10-2=8.

The third term, f (3), is 8-2=6.