Geometric series applications practice quiz for Algebra 2 students

📚 Topic Summary

A geometric series is the sum of the terms of a geometric sequence. Understanding geometric series is crucial for various applications, including calculating compound interest, analyzing population growth, and determining the total distance traveled by a bouncing ball. This worksheet will provide you with practice problems to master these applications.

🧮 Part A: Vocabulary

Match the following terms with their correct definitions:

1. Term: A) The ratio between consecutive terms in a geometric sequence.
2. Common Ratio: B) The sum of an infinite geometric sequence with $|r| < 1$.
3. Geometric Sequence: C) A sequence where each term is multiplied by a constant to get the next term.
4. Geometric Series: D) Each individual number in a sequence.
5. Infinite Geometric Series: E) The sum of the terms in a geometric sequence.

Answers: 1-D, 2-A, 3-C, 4-E, 5-B

✍️ Part B: Fill in the Blanks

Complete the following paragraph with the correct terms:

A __________ sequence is a sequence where each term is multiplied by a constant called the __________. The sum of the terms in this sequence forms a __________. If the absolute value of the common ratio is less than 1, the __________ can be calculated even for an infinite number of terms. This concept is useful in various real-world __________.

Possible Answers: geometric, common ratio, geometric series, sum, applications

🤔 Part C: Critical Thinking

Explain how understanding geometric series can help in making financial decisions related to investments or loans. Provide a specific example.