The image shows a question asking to use inductive reasoning to determine the next two terms in two sequences:

Sequence a:

$1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dots$ This sequence is a geometric progression where each term is multiplied by $\frac{1}{2}$.

• To get the next term: $\frac{1}{16} \times \frac{1}{2} = \frac{1}{32}$
• The term after that: $\frac{1}{32} \times \frac{1}{2} = \frac{1}{64}$ Thus, the next two terms are $\frac{1}{32}$ and $\frac{1}{64}$.

Sequence b:

$A, B, D, G, K, \dots$ This sequence progresses by skipping letters in the alphabet:

• After A (no skip), the next is B.
• After B, skip C and get to D.
• After D, skip E and F, and arrive at G.
• After G, skip H, I, J, and get to K.

Following this pattern:

• After K, skip L, M, N, and the next letter is O.
• After O, skip P, Q, R, and the next letter is S.

So, the next two letters are O and S.

Would you like more details or explanations on these sequences?

Here are 5 related questions:

1. What is inductive reasoning, and how is it applied in pattern recognition?
2. How do you identify geometric progressions, and what are their properties?
3. Can a letter sequence follow a different logic than skipping letters? If so, how would you identify it?
4. How do arithmetic progressions differ from geometric progressions?
5. What role do exponents play in sequences like part a?

Tip: When working with letter sequences, visualize the alphabet or write it down to better identify skipping patterns.