Question

Use inductive reasoning to describe the pattern of each sequence. Then find the

next two terms.
8, 3, 9, 4, 10, 5,...

Answer 1

The sequence alternates between increasing even and odd numbers, so following this pattern, the next two terms are 11 and 6.

Step-by-step explanation:

Using inductive reasoning to describe the sequence 8, 3, 9, 4, 10, 5, we can observe a pattern where each even-indexed term (starting from index 1) is an increasing even number starting at 8, and each odd-indexed term is an increasing odd number starting at 3. The sequence alternates between adding 1 to the even number and adding 1 to the odd number.

To find the next two terms, we follow the established pattern:

1. The term after 5 should be an even number following 10, which is 11.
2. Then we have an odd number following 11, so the next term would be 6.

Therefore, the next two terms in the sequence are 11 and 6.