The image you've uploaded contains a set of questions about sequences. Let me help explain the answers to each of these:

a) An infinite sequence is: A sequence whose domain is the set of positive integers.

b) Each number in the list is called: A term.

c) A sequence {aₙ} where aₙ = c rⁿ for some non-zero constants c and r is called: A geometric sequence.

d) Which of the following statements are true or false?

• The index of a sequence must start at n = 1.
  Answer: False. The index of a sequence can start at any integer (e.g., n = 0 or n = 5), though starting at n = 1 is common.

• If a sequence {aₙ} is given by aₙ = 1/3ⁿ, then the 5th number in the sequence is 1/243.
  Answer: True. If aₙ = 1/3ⁿ, then for n = 5, a₅ = 1/3⁵ = 1/243.

• If a sequence {aₙ} is given by aₙ = (-1)ⁿ/2ⁿ, then every second number in the sequence is positive, and every other number is negative.
  Answer: True. The factor (-1)ⁿ alternates the sign between positive and negative with each term. Since n alternates between even and odd, every second term will alternate between positive and negative values.

• If a sequence {aₙ} is given by aₙ = 1 + (-1)ⁿ/n, then every second number in the sequence is positive, and every other number is negative.
  Answer: False. In this case, the term depends on the alternating sign from (-1)ⁿ. For even n, the sign is positive, and for odd n, it is negative. However, the behavior of the sequence differs because the term is also divided by n, which makes it decay toward zero as n increases.

• A sequence can be thought of as a function whose domain is the set of positive integers.
  Answer: True. A sequence is a function where the domain consists of positive integers (1, 2, 3, ...).

Do you have any questions or need further clarification on any part of this? Feel free to ask!

Here are some related questions to explore further:

1. What is the general formula for a geometric sequence?
2. How can sequences be used in real-world applications like finance or physics?
3. What does it mean for a sequence to converge or diverge?
4. Can the index of a sequence start at other values besides 1? Provide an example.
5. How do alternating sequences work, and where are they commonly used?

Tip: When dealing with geometric sequences, the ratio between consecutive terms is constant. This ratio is key to identifying and analyzing geometric sequences.