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**Exercise Instructions for Sequence Terms** For Exercises 1 through 3, write out the first five terms of each sequence. 1. **Sequence A:** - Initial condition: \( A(1) = 2 \) - Recursive formula: \( A(n) = \frac{1}{A(n-1)} \) for \( n \geq 2 \). 2. **Sequence P:** - Initial condition: \( P(1) = 1 \) - Recursive formula: \( P(n) = n^2 P(n-1) + (n-1) \) for \( n \geq 2 \). 3. **Sequence T:** - Initial condition for \( n \leq 3 \): \( T(n) = n \) - Recursive formula: \( T(n) = T(n-1) + 2T(n-2) + 3T(n-3) \) for \( n \geq 4 \). For each sequence, apply the given conditions and formulas to find and write out the first five terms.

**Exercise Instructions for Sequence Terms** For Exercises 1 through 3, write out the first five terms of each sequence. 1. **Sequence A:** - Initial condition: \( A(1) = 2 \) - Recursive formula: \( A(n) = \frac{1}{A(n-1)} \) for \( n \geq 2 \). 2. **Sequence P:** - Initial condition: \( P(1) = 1 \) - Recursive formula: \( P(n) = n^2 P(n-1) + (n-1) \) for \( n \geq 2 \). 3. **Sequence T:** - Initial condition for \( n \leq 3 \): \( T(n) = n \) - Recursive formula: \( T(n) = T(n-1) + 2T(n-2) + 3T(n-3) \) for \( n \geq 4 \). For each sequence, apply the given conditions and formulas to find and write out the first five terms.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Exercise Instructions for Sequence Terms** For Exercises 1 through 3, write out the first five terms of each sequence. 1. **Sequence A:** - Initial condition: \( A(1) = 2 \) - Recursive formula: \( A(n) = \frac{1}{A(n-1)} \) for \( n \geq 2 \). 2. **Sequence P:** - Initial condition: \( P(1) = 1 \) - Recursive formula: \( P(n) = n^2 P(n-1) + (n-1) \) for \( n \geq 2 \). 3. **Sequence T:** - Initial condition for \( n \leq 3 \): \( T(n) = n \) - Recursive formula: \( T(n) = T(n-1) + 2T(n-2) + 3T(n-3) \) for \( n \geq 4 \). For each sequence, apply the given conditions and formulas to find and write out the first five terms.
Transcribed Image Text:**Exercise Instructions for Sequence Terms** For Exercises 1 through 3, write out the first five terms of each sequence. 1. **Sequence A:** - Initial condition: \( A(1) = 2 \) - Recursive formula: \( A(n) = \frac{1}{A(n-1)} \) for \( n \geq 2 \). 2. **Sequence P:** - Initial condition: \( P(1) = 1 \) - Recursive formula: \( P(n) = n^2 P(n-1) + (n-1) \) for \( n \geq 2 \). 3. **Sequence T:** - Initial condition for \( n \leq 3 \): \( T(n) = n \) - Recursive formula: \( T(n) = T(n-1) + 2T(n-2) + 3T(n-3) \) for \( n \geq 4 \). For each sequence, apply the given conditions and formulas to find and write out the first five terms.
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