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What are the first 5 terms of the sequence represented by a=2n-3a n "n-1, where a₁ = 4₂

What are the first 5 terms of the sequence represented by a=2n-3a n "n-1, where a₁ = 4₂

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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### Question 26 **Problem Statement:** What are the first 5 terms of the sequence represented by the recurrence relation: \[ a_n = 2n - 3a_{n-1} \] where \[ a_1 = 4 \] **Solution:** To find the first five terms of this sequence, we'll start with the initial term and apply the recurrence relation to find subsequent terms. 1. The first term is given: \[ a_1 = 4 \] 2. Now, we calculate the second term using the recurrence relation \( a_n = 2n - 3a_{n-1} \): \[ a_2 = 2(2) - 3a_1 \] \[ a_2 = 4 - 3(4) \] \[ a_2 = 4 - 12 \] \[ a_2 = -8 \] 3. Next, we calculate the third term: \[ a_3 = 2(3) - 3a_2 \] \[ a_3 = 6 - 3(-8) \] \[ a_3 = 6 + 24 \] \[ a_3 = 30 \] 4. For the fourth term: \[ a_4 = 2(4) - 3a_3 \] \[ a_4 = 8 - 3(30) \] \[ a_4 = 8 - 90 \] \[ a_4 = -82 \] 5. Finally, the fifth term: \[ a_5 = 2(5) - 3a_4 \] \[ a_5 = 10 - 3(-82) \] \[ a_5 = 10 + 246 \] \[ a_5 = 256 \] Therefore, the first 5 terms of the sequence are: \[ 4, -8, 30, -82, 256 \]
Transcribed Image Text:### Question 26 **Problem Statement:** What are the first 5 terms of the sequence represented by the recurrence relation: \[ a_n = 2n - 3a_{n-1} \] where \[ a_1 = 4 \] **Solution:** To find the first five terms of this sequence, we'll start with the initial term and apply the recurrence relation to find subsequent terms. 1. The first term is given: \[ a_1 = 4 \] 2. Now, we calculate the second term using the recurrence relation \( a_n = 2n - 3a_{n-1} \): \[ a_2 = 2(2) - 3a_1 \] \[ a_2 = 4 - 3(4) \] \[ a_2 = 4 - 12 \] \[ a_2 = -8 \] 3. Next, we calculate the third term: \[ a_3 = 2(3) - 3a_2 \] \[ a_3 = 6 - 3(-8) \] \[ a_3 = 6 + 24 \] \[ a_3 = 30 \] 4. For the fourth term: \[ a_4 = 2(4) - 3a_3 \] \[ a_4 = 8 - 3(30) \] \[ a_4 = 8 - 90 \] \[ a_4 = -82 \] 5. Finally, the fifth term: \[ a_5 = 2(5) - 3a_4 \] \[ a_5 = 10 - 3(-82) \] \[ a_5 = 10 + 246 \] \[ a_5 = 256 \] Therefore, the first 5 terms of the sequence are: \[ 4, -8, 30, -82, 256 \]
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