🔢 Topic Summary
In mathematics, a sequence is an ordered list of numbers. Sequence notation provides a concise way to represent these numbers. We often use $a_n$ to denote the $n$-th term of a sequence, where $n$ is a positive integer. For example, $a_1$ is the first term, $a_2$ is the second term, and so on.
Another way to represent sequences is using function notation, $f(n)$. In this case, $f(n)$ gives the $n$-th term of the sequence. The variable $n$ represents the position of the term in the sequence. Both $a_n$ and $f(n)$ notations are interchangeable and represent the same concept: defining a sequence based on the position of its terms.
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Sequence |
A. The position of a term in a sequence |
| 2. $a_n$ |
B. A function that defines the terms of a sequence |
| 3. $f(n)$ |
C. The $n$-th term of a sequence |
| 4. $n$ |
D. An ordered list of numbers |
| 5. Term |
E. A single number in a sequence |
Match the numbers with the correct letters: 1-?, 2-?, 3-?, 4-?, 5-?
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: sequence, $n$-th, $f(n)$, $a_n$, term.
A __________ is an ordered list of numbers. The __________ term of a sequence can be represented by __________ or __________. Each number in the sequence is called a __________.
🤔 Part C: Critical Thinking
Explain, in your own words, the difference between $a_n$ and $f(n)$ notation. Are they truly different, or are they just different ways of expressing the same thing?