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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