A sequence is defined by the formula fn = 1 + fn-3. If f4 = 22, what is f1?

To solve for f1 in the sequence defined by the formula fn = 1 + fn-3, we start by using the given information that f4 = 22.

Using the formula:

• To find f4, we need f1 since it relies on the previous terms.
• From the formula, we can express f4 as:
• f4 = 1 + f1 when n=4,
• Thus, we can write 22 = 1 + f1.

Now, we can solve for f1:

• f1 = 22 – 1
• f1 = 21

So, the value of f1 is 21.