Start with any odd number `n`, multiply by `n + 4` for the third, then by `n + 6` for the fourth. Boom, product!
We can find the product of the third and fourth consecutive odd integers without listing them using a simple formula:
1. Choose any odd integer as a starting point. Let's call this integer `n`.
2. Recognize that the next odd integer in the sequence is `n + 2`.
3. The third consecutive odd integer is then `n + 4` (adding two more to `n + 2`).
4. Similarly, the fourth consecutive odd integer is `n + 6`.
5. Therefore, the product of the third and fourth odd integers is simply `(n + 4) * (n + 6)`.
This formula works because it captures the relationship between consecutive odd integers: each odd integer is 2 more than the previous one. By multiplying the third and fourth odd integers (`n + 4` and `n + 6`), we avoid the need to list out the entire sequence.
Question:
How can you find the product of the third and fourth consecutive odd integers without explicitly listing them?