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1. Find the first 5 terms of the sequence from the recurrence relation. Given: • a = 3 a, = 6 a = a n-1 4a n-2 Show your work here: az = a Then, write down the first 5 terms of the sequence: What is the 7th term in the pattem above? a. a

1. Find the first 5 terms of the sequence from the recurrence relation. Given: • a = 3 a, = 6 a = a n-1 4a n-2 Show your work here: az = a Then, write down the first 5 terms of the sequence: What is the 7th term in the pattem above? a. a

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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### Problem Statement: 1. **Find the first 5 terms of the sequence from the recurrence relation. Given:** - \( a_0 = 3 \) - \( a_1 = 6 \) - \( a_n = a_{n-1} + 4a_{n-2} \) ### Steps to Solve: - **Calculate \( a_2 \):** - \( a_2 = a_1 + 4a_0 = 6 + 4 \times 3 = 18 \) - **Calculate \( a_3 \):** - \( a_3 = a_2 + 4a_1 = 18 + 4 \times 6 = 42 \) - **Calculate \( a_4 \):** - \( a_4 = a_3 + 4a_2 = 42 + 4 \times 18 = 114 \) ### Sequence: - **Write down the first 5 terms of the sequence:** - \( a_0 = 3 \) - \( a_1 = 6 \) - \( a_2 = 18 \) - \( a_3 = 42 \) - \( a_4 = 114 \) ### Further Question: - **What is the 7th term in the pattern above?** - **Calculate \( a_5 \):** - \( a_5 = a_4 + 4a_3 = 114 + 4 \times 42 = 282 \) - **Calculate \( a_6 \):** - \( a_6 = a_5 + 4a_4 = 282 + 4 \times 114 = 738 \)
Transcribed Image Text:### Problem Statement: 1. **Find the first 5 terms of the sequence from the recurrence relation. Given:** - \( a_0 = 3 \) - \( a_1 = 6 \) - \( a_n = a_{n-1} + 4a_{n-2} \) ### Steps to Solve: - **Calculate \( a_2 \):** - \( a_2 = a_1 + 4a_0 = 6 + 4 \times 3 = 18 \) - **Calculate \( a_3 \):** - \( a_3 = a_2 + 4a_1 = 18 + 4 \times 6 = 42 \) - **Calculate \( a_4 \):** - \( a_4 = a_3 + 4a_2 = 42 + 4 \times 18 = 114 \) ### Sequence: - **Write down the first 5 terms of the sequence:** - \( a_0 = 3 \) - \( a_1 = 6 \) - \( a_2 = 18 \) - \( a_3 = 42 \) - \( a_4 = 114 \) ### Further Question: - **What is the 7th term in the pattern above?** - **Calculate \( a_5 \):** - \( a_5 = a_4 + 4a_3 = 114 + 4 \times 42 = 282 \) - **Calculate \( a_6 \):** - \( a_6 = a_5 + 4a_4 = 282 + 4 \times 114 = 738 \)
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