Let's analyze each sequence and find the pattern to continue them:

a. 3, 5, 7, 9, ...

• This sequence increments by 2:
  • $5 - 3 = 2$, $7 - 5 = 2$, and $9 - 7 = 2$.
• The next number will be $9 + 2 = 11$.

b. 4, 16, 32, 64, ...

• This sequence is doubling the previous term:
  • $16 = 4 \times 4$, $32 = 16 \times 2$, $64 = 32 \times 2$.
• The next number will be $64 \times 2 = 128$.

c. 2, 3, 6, 7, ...

• The pattern alternates between adding 1 and multiplying by 2:
  • $3 = 2 + 1$, $6 = 3 \times 2$, $7 = 6 + 1$.
• The next number will be $7 \times 2 = 14$.

d. 5, 10, 11, 22, ...

• The pattern alternates between multiplying by 2 and adding 1:
  • $10 = 5 \times 2$, $11 = 10 + 1$, $22 = 11 \times 2$.
• The next number will be $22 + 1 = 23$.

e. 81, 27, 9, 3, ...

• This sequence divides by 3 each time:
  • $81 \div 3 = 27$, $27 \div 3 = 9$, $9 \div 3 = 3$.
• The next number will be $3 \div 3 = 1$.

To summarize, the next numbers in each sequence are:

• a: $11$
• b: $128$
• c: $14$
• d: $23$
• e: $1$

Would you like further details or have any questions?

Here are 5 related questions to expand on the above:

1. What kind of sequence would result from alternating addition and subtraction?
2. How would the sequence change if instead of doubling, you tripled the terms?
3. What happens if you modify sequence (a) by increasing the step size?
4. Can you identify a real-life situation where a division sequence like (e) occurs?
5. How would the pattern in sequence (d) change if you reversed the operations?

Tip: When analyzing a number sequence, always check for common operations like addition, multiplication, or division, as these often form the basis of the pattern.