TMN3705 Assignment 2 Due 26 August 2024

QUESTION 1
You are starting a unit on geometric sequences. After you have provided several examples,
you are faced with a learner’s question.

1.1 Behaviourist Approach Dialogue
Learner: What is GEOMETRIC about geometric sequences?
Teacher: What do you mean?
Learner: You called these sequences “geometric”, but these are just sequences of
numbers.
Teacher: I understand your question. Let’s look at the definition. A geometric sequence is a
sequence of numbers where each term after the first is found by multiplying the previous
term by a fixed, non-zero number called the common ratio.
Learner: So, it’s called geometric because of the multiplication?
Teacher: Exactly. For example, in the sequence 2, 6, 18, 54, each term is multiplied by 3 to
get the next term. This constant multiplication is what makes it a geometric sequence. Let’s
practice identifying the common ratio in different sequences.