### Geometric Series - Independent Practice #11. **Problem Statement:** - When a rubber ball is dropped from a height of 1,280 centimeters, the heights in centimeters of the first few bounces form a geometric sequence: - 960, 720, _______, _______ a) **Question:** What is the common ratio of this sequence? **Answer Box:** - [ ]2. **Follow-Up Question:** - Find the heights of the third and fourth bounces.**Explanation for Teachers and Students:**This exercise focuses on understanding and calculating the terms of a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.**Given Sequence:**- First term ($a_1$) = 1280 cm- Second term ($a_2$) = 960 cm- Third term ($a_3$) = 720 cmTo solve part (a), you need to find the common ratio ($r$) using the terms provided. Once the common ratio is determined, apply it to find the missing terms in the sequence.**Mathematical Approach:**1. **Calculate the Common Ratio:** $r = \frac{a_2}{a_1} = \frac{960}{1280} = 0.75$ $r = \frac{a_3}{a_2} = \frac{720}{960} = 0.75$2. **Identify the Missing Terms:** - Third term ($a_4$): $720 \times 0.75$ - Fourth term ($a_5$): $a_4 \times 0.75$By following these steps, students will be able to complete the sequence and identify the common ratio correctly. Encourage them to practice with different sequences to reinforce their understanding of geometric progressions. ### Bouncing Ball Height Problem#### Question 1**Prompt:** Find the heights of the third and fourth bounces.*Response Area**[Empty Text Box]*#### Question 2**Prompt:** Write a sequence definition to define the height of the ball after *n* bounces.*Response Area**[Empty Text Box]**Note:* No graphs or diagrams are present in the image.#### SubmissionA "Submit" button is visible at the bottom right of the interface, presumably for students to submit their responses once they have completed the tasks in the text boxes provided.

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Description: ### Geometric Series - Independent Practice #11. **Problem Statement:** - When a rubber ball is dropped from a height of 1,280 centimeters, the heights in centimeters of the first few bounces form a geometric sequence: - 960, 720, _______, ___

Math

Algebra

etric Independent Practice #1 1. When a rubber ball is dropped from a height of 1,280 centimeters, the heights in centimeters of the first few bounces form a geometric sequence: 960, 720, a) What is the common ratio of this sequence? Find the heights of the third and fourth bounces.

etric Independent Practice #1 1. When a rubber ball is dropped from a height of 1,280 centimeters, the heights in centimeters of the first few bounces form a geometric sequence: 960, 720, a) What is the common ratio of this sequence? Find the heights of the third and fourth bounces.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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