📚 Topic Summary
Sequences are ordered lists of numbers, while series are the sums of those numbers. In the real world, sequences and series can model everything from compound interest and loan repayments to the heights of bouncing balls and the decay of radioactive materials. Understanding these concepts helps us predict future outcomes and make informed decisions. Let's dive into some practical examples!
🧮 Part A: Vocabulary
Match each term with its correct definition:
| Term |
Definition |
| 1. Arithmetic Sequence |
A. The sum of the terms in a sequence. |
| 2. Geometric Sequence |
B. A sequence where the ratio between consecutive terms is constant. |
| 3. Common Difference |
C. A sequence where the difference between consecutive terms is constant. |
| 4. Common Ratio |
D. The constant value multiplied by each term to get the next term in a geometric sequence. |
| 5. Series |
E. The constant value added to each term to get the next term in an arithmetic sequence. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided: finite, infinite, sum, term, sequence.
A _______ is an ordered list of numbers. Each number in the list is called a _______. If the sequence has a last number, it is a _______ sequence. Otherwise, it is an _______ sequence. A series is the _______ of the terms in a sequence.
🤔 Part C: Critical Thinking
Imagine you're offered two jobs. Job A starts at $50,000 per year with a guaranteed $3,000 raise each year. Job B starts at $45,000 per year with a guaranteed 6% raise each year. Which job would pay you more after 10 years? Explain your reasoning, showing all work. Which pays more after 20 years?