Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Find the first 5 terms of the sequence from the recurrence relation. Given: • a, = 5, • az = 6, • a, = an-1+ 4an-2 %3D a (5, 6, 26, 50, 152) b (5, 6, 26, 50, 154} (5, 6, 26, 51, 154) {5, 6, 27, 50, 154}

Find the first 5 terms of the sequence from the recurrence relation. Given: • a, = 5, • az = 6, • a, = an-1+ 4an-2 %3D a (5, 6, 26, 50, 152) b (5, 6, 26, 50, 154} (5, 6, 26, 51, 154) {5, 6, 27, 50, 154}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
**Problem Statement:** Find the first 5 terms of the sequence from the recurrence relation. Given: - \( a_0 = 5 \), - \( a_1 = 6 \), - \( a_n = a_{n-1} + 4a_{n-2} \) **Options:** - a) \(\{5, 6, 26, 50, 152\}\) - b) \(\{5, 6, 26, 50, 154\}\) - c) \(\{5, 6, 26, 51, 154\}\) - d) \(\{5, 6, 27, 50, 154\}\) **Explanation:** You need to generate the terms of the sequence using the given recurrence relation. Start with the initial values \( a_0 = 5 \) and \( a_1 = 6 \), then use the formula \( a_n = a_{n-1} + 4a_{n-2} \) to calculate the subsequent terms. 1. \( a_0 = 5 \) 2. \( a_1 = 6 \) 3. Calculate \( a_2 \): \( a_2 = a_1 + 4a_0 = 6 + 4 \times 5 = 6 + 20 = 26 \) 4. Calculate \( a_3 \): \( a_3 = a_2 + 4a_1 = 26 + 4 \times 6 = 26 + 24 = 50 \) 5. Calculate \( a_4 \): \( a_4 = a_3 + 4a_2 = 50 + 4 \times 26 = 50 + 104 = 154 \) Based on the above calculations, the correct sequence is: - b) \(\{5, 6, 26, 50, 154\}\)
Transcribed Image Text:**Problem Statement:** Find the first 5 terms of the sequence from the recurrence relation. Given: - \( a_0 = 5 \), - \( a_1 = 6 \), - \( a_n = a_{n-1} + 4a_{n-2} \) **Options:** - a) \(\{5, 6, 26, 50, 152\}\) - b) \(\{5, 6, 26, 50, 154\}\) - c) \(\{5, 6, 26, 51, 154\}\) - d) \(\{5, 6, 27, 50, 154\}\) **Explanation:** You need to generate the terms of the sequence using the given recurrence relation. Start with the initial values \( a_0 = 5 \) and \( a_1 = 6 \), then use the formula \( a_n = a_{n-1} + 4a_{n-2} \) to calculate the subsequent terms. 1. \( a_0 = 5 \) 2. \( a_1 = 6 \) 3. Calculate \( a_2 \): \( a_2 = a_1 + 4a_0 = 6 + 4 \times 5 = 6 + 20 = 26 \) 4. Calculate \( a_3 \): \( a_3 = a_2 + 4a_1 = 26 + 4 \times 6 = 26 + 24 = 50 \) 5. Calculate \( a_4 \): \( a_4 = a_3 + 4a_2 = 50 + 4 \times 26 = 50 + 104 = 154 \) Based on the above calculations, the correct sequence is: - b) \(\{5, 6, 26, 50, 154\}\)
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS