📚 Topic Summary
An arithmetic sequence is a list of numbers where the difference between any two consecutive terms is constant. This constant difference is called the 'common difference'. To find the $n$th term ($a_n$) of an arithmetic sequence, you can use the formula: $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference. Understanding these basics unlocks your ability to predict any term in the sequence!
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Arithmetic Sequence |
A. The term you are trying to find in the sequence. |
| 2. Common Difference |
B. The first number in the sequence. |
| 3. $n$th Term |
C. A sequence where the difference between consecutive terms is constant. |
| 4. First Term ($a_1$) |
D. The constant difference between consecutive terms in an arithmetic sequence. |
| 5. $n$ |
E. The position of a term in the sequence. |
✍️ Part B: Fill in the Blanks
An arithmetic sequence is a list of __________ where the difference between consecutive terms is __________. This difference is called the __________ __________. The formula to find the $n$th term is $a_n = a_1 + (n - 1)d$, where $a_1$ is the __________ term, $n$ is the __________ number, and $d$ is the __________ __________.
🤔 Part C: Critical Thinking
Explain in your own words how you would determine if a given sequence is arithmetic. What steps would you take, and what are you looking for?