The question asks for the next term in each of two sequences:

Sequence (a):

The given terms are: 16, 25, 36, 49, ...

Notice that each term seems to be the square of a number:

• $16 = 4^2$
• $25 = 5^2$
• $36 = 6^2$
• $49 = 7^2$

The next term will be $8^2 = 64$.

Sequence (b):

The given terms are: 8, 27, 64, 125, ...

These numbers appear to be cubes of integers:

• $8 = 2^3$
• $27 = 3^3$
• $64 = 4^3$
• $125 = 5^3$

The next term will be $6^3 = 216$.

Answers:

• For (a): The next term is 64.
• For (b): The next term is 216.

Would you like more details on the steps, or do you have any other questions?

Here are some follow-up questions to explore:

1. How do you identify patterns in a sequence of numbers?
2. Can you find another way to calculate squares and cubes of numbers quickly?
3. What are arithmetic and geometric sequences, and how do they differ from these examples?
4. How would the sequence change if each term was increased by a constant number?
5. What happens if we apply these patterns to sequences involving negative numbers?

Tip: When recognizing patterns, checking powers like squares or cubes can quickly reveal mathematical relationships in sequences.