Question

Write the next two apparent terms of the sequence. Describe the pattern you used to find these terms. \(\frac{7}{2}, 4, \frac{9}{2}, 5, \ldots\)

Short answer

The next two terms in the sequence are: 5.5, 6

Step-by-step solution

Identifying the Pattern

First, rewrite the whole numbers as fractions: \(\frac{7}{2}, \frac{8}{2}, \frac{9}{2}, \frac{10}{2}\). Now, it becomes clear that the numerator of the fraction is incrementing by 1 for each subsequent term.

Finding the Next Term

To find the next term, we increase the numerator of the last known term (which is 10) by 1, making it 11. So, the next term would be \(\frac{11}{2}\) or 5.5 when written in decimal form.

Finding the Second Next Term

Following the same method, to find the term after \(\frac{11}{2}\), we will increase the numerator by 1, making it 12. So, the subsequent term will be \(\frac{12}{2}\), which simplifies to 6.