An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference. In simpler terms, you start with a number, and then keep adding or subtracting the same number to get the next number in the sequence. Arithmetic sequences can be found all around us, from the number of seats in a stadium to the way a savings account grows with regular deposits. Understanding arithmetic sequences helps in predicting patterns and solving various real-world problems.
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Common Difference | A. The sum of the terms in an arithmetic sequence. |
| 2. Arithmetic Sequence | B. A sequence where the difference between consecutive terms is constant. |
| 3. Term | C. A specific number in a sequence. |
| 4. First Term | D. The difference between consecutive terms in an arithmetic sequence. |
| 5. Arithmetic Series | E. The initial value in an arithmetic sequence. |
An arithmetic sequence is a sequence where the _______ between consecutive terms is _______. This constant difference is called the _______ _______. To find the next term, you _______ the common difference to the previous term. The general formula to find the $n^{th}$ term ($a_n$) of an arithmetic sequence is $a_n = a_1 + (n-1)d$, where $a_1$ is the _______ _______ and $d$ is the common difference.
Imagine you are designing seating for a theater. The first row has 20 seats, and each subsequent row has 2 more seats than the row before it. How can you use the concept of arithmetic sequences to determine the number of seats in the 10th row? Explain your approach.
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