Write a recursive sequence that represents the sequence defined by the following explicit formula: An = -4 - 3n an Submit Answer an 1

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Title: Writing Recursive Sequences from Explicit Formulas**

**Task Description:**

Write a recursive sequence that represents the sequence defined by the following explicit formula:

\[ a_n = -4 - 3n \]

**Interactive Exercise:**

Fill in the values for the initial term and the recursive formula of the sequence.

**Input Fields:**

1. \( a_1 = \) [Input Box]
2. \( a_n = \) [Input Box]

**Button:**

[Submit Answer]

**Note:**

- Ensure you properly understand how to construct a recursive formula from an explicit one before submitting your answers.
- The initial term (\( a_1 \)) should align with the formula given for \( n = 1 \).
- The recursive formula should describe how to get the nth term from the (n-1)th term.

**Example Calculation:**

For the explicit formula \( a_n = -4 - 3n \), find the corresponding recursive form.

1. Calculate the first term:
    \[ a_1 = -4 - 3(1) = -4 - 3 = -7 \]
2. Identify the relationship between consecutive terms:
    \[ a_{n+1} = a_n - 3 \]

Therefore, the recursive sequence is:
\[ a_1 = -7 \]
\[ a_n = a_{n-1} - 3 \] for \( n > 1 \)

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Transcribed Image Text:**Title: Writing Recursive Sequences from Explicit Formulas** **Task Description:** Write a recursive sequence that represents the sequence defined by the following explicit formula: \[ a_n = -4 - 3n \] **Interactive Exercise:** Fill in the values for the initial term and the recursive formula of the sequence. **Input Fields:** 1. \( a_1 = \) [Input Box] 2. \( a_n = \) [Input Box] **Button:** [Submit Answer] **Note:** - Ensure you properly understand how to construct a recursive formula from an explicit one before submitting your answers. - The initial term (\( a_1 \)) should align with the formula given for \( n = 1 \). - The recursive formula should describe how to get the nth term from the (n-1)th term. **Example Calculation:** For the explicit formula \( a_n = -4 - 3n \), find the corresponding recursive form. 1. Calculate the first term: \[ a_1 = -4 - 3(1) = -4 - 3 = -7 \] 2. Identify the relationship between consecutive terms: \[ a_{n+1} = a_n - 3 \] Therefore, the recursive sequence is: \[ a_1 = -7 \] \[ a_n = a_{n-1} - 3 \] for \( n > 1 \) **Privacy Policy** | **Terms of Service** **Copyright © 2021 DeltaMath.com. All Rights Reserved.**
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