📚 Topic Summary
In mathematics, a sequence is an ordered list of numbers or other elements. Sequence notation, particularly $a_n$, is a way to represent these sequences. The term $a_n$ refers to the 'n-th' term in the sequence. For instance, if we have a sequence defined by $a_n = 2n + 1$, then $a_1$ would be the first term (2(1) + 1 = 3), $a_2$ would be the second term (2(2) + 1 = 5), and so on. Understanding this notation is crucial for working with arithmetic, geometric, and other types of sequences.
This activity will help you become familiar with this notation and how to use it to find specific terms in a sequence.
🧮 Part A: Vocabulary
Match the term with its correct definition.
| Term |
Definition |
| 1. Sequence |
A. The general formula that defines a sequence. |
| 2. Term |
B. A function whose domain is the set of natural numbers. |
| 3. $a_n$ |
C. A specific number in a sequence. |
| 4. Explicit Formula |
D. The 'n-th' term of a sequence. |
| 5. Index |
E. The position of a term in a sequence. |
✍️ Part B: Fill in the Blanks
A ______ is an ordered list of elements, usually numbers. Each element in the sequence is called a ______. The notation $a_n$ represents the ______ term of the sequence, where 'n' is the ______. An ______ formula defines the sequence directly in terms of 'n'.
🤔 Part C: Critical Thinking
Consider two sequences: $a_n = 3n - 1$ and $b_n = n^2$. For what value(s) of 'n' is $a_n > b_n$?