Write down the first five terms of the following recursively defined sequence. a1 = 5; an+1=-2a, – 8 5
Write down the first five terms of the following recursively defined sequence. a1 = 5; an+1=-2a, – 8 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Instructions:**
Write down the first five terms of the following recursively defined sequence.
\[ a_1 = 5; \quad a_{n+1} = -2a_n - 8 \]
**Solution:**
1. \( a_1 = 5 \)
Now apply the recursive formula to find the subsequent terms:
2. \( a_2 = -2(5) - 8 = -10 - 8 = -18 \)
3. \( a_3 = -2(-18) - 8 = 36 - 8 = 28 \)
4. \( a_4 = -2(28) - 8 = -56 - 8 = -64 \)
5. \( a_5 = -2(-64) - 8 = 128 - 8 = 120 \)
**First five terms:**
\[ 5, -18, 28, -64, 120 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76b39ad3-98e6-4bd8-afd7-9890d91d962f%2F8b1c1f3e-99bc-4233-a5e5-bd751de3b58e%2Fd42nccd_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions:**
Write down the first five terms of the following recursively defined sequence.
\[ a_1 = 5; \quad a_{n+1} = -2a_n - 8 \]
**Solution:**
1. \( a_1 = 5 \)
Now apply the recursive formula to find the subsequent terms:
2. \( a_2 = -2(5) - 8 = -10 - 8 = -18 \)
3. \( a_3 = -2(-18) - 8 = 36 - 8 = 28 \)
4. \( a_4 = -2(28) - 8 = -56 - 8 = -64 \)
5. \( a_5 = -2(-64) - 8 = 128 - 8 = 120 \)
**First five terms:**
\[ 5, -18, 28, -64, 120 \]
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