# A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. if f(1) = 18, what is f(5)?

The given recursive formula f(n + 1) = f(n) – 2 tells us that to find the (n + 1)th term of the sequence, we subtract 2 from the nth term. In simpler terms, each term in the sequence is obtained by subtracting 2 from the previous term. Now, let’s apply this formula to solve for f(5) using the initial condition f(1) = 18.

## Solving for f(5) Using the Recursive Formula

To solve for f(5), we need to determine the values of the sequence up to the 5th term. Let’s go step by step:

### Step 1: Finding f(2)

Using the given formula, we subtract 2 from f(1): f(2) = f(1) – 2 = 18 – 2 = 16

### Step 2: Finding f(3)

Applying the formula once again, we subtract 2 from f(2): f(3) = f(2) – 2 = 16 – 2 = 14

### Step 3: Finding f(4)

Continuing the pattern, we subtract 2 from f(3): f(4) = f(3) – 2 = 14 – 2 = 12

### Step 4: Finding f(5)

Finally, we find the 5th term of the sequence by subtracting 2 from f(4): f(5) = f(4) – 2 = 12 – 2 = 10

Therefore, f(5) is equal to 10.

### What is a Recursive Sequence?

In mathematics, a recursive sequence is a sequence in which each term is obtained by applying a specific rule or formula to the previous terms. This self-referential nature makes recursive sequences intriguing and allows us to model various real-life phenomena.

### Can recursive sequences have different formulas for different terms?

Yes, recursive sequences can have different formulas for different terms, depending on the specific pattern or rule governing the sequence.

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