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Give a recursive definition of the following sequences (an)n≥1. Put the appropriate letter next to the corresponding sequence. 1. an 2. An 3. An = = 4. an = 6 6n + 1 6n 6n a) An+1 = an + 6 for n ≥ 1 and a₁ = 6 b) an+1 =an for n ≥ 1 and 1 6 = c) an+1 = an +6 for n ≥ 1 and a₁ = 7 d) an+1 = 6an for n ≥1 and a₁ = 6

Give a recursive definition of the following sequences (an)n≥1. Put the appropriate letter next to the corresponding sequence. 1. an 2. An 3. An = = 4. an = 6 6n + 1 6n 6n a) An+1 = an + 6 for n ≥ 1 and a₁ = 6 b) an+1 =an for n ≥ 1 and 1 6 = c) an+1 = an +6 for n ≥ 1 and a₁ = 7 d) an+1 = 6an for n ≥1 and a₁ = 6

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
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**Problem Statement:** Give a recursive definition of the following sequences \((a_n)_{n \geq 1}\). Put the appropriate letter next to the corresponding sequence. 1. \( a_n = 6 \) 2. \( a_n = 6n + 1 \) 3. \( a_n = 6^n \) 4. \( a_n = 6n \) **Recursive Definitions:** a) \( a_{n+1} = a_n + 6 \) for \( n \geq 1 \) and \( a_1 = 6 \) b) \( a_{n+1} = a_n \) for \( n \geq 1 \) and \( a_1 = 6 \) c) \( a_{n+1} = a_n + 6 \) for \( n \geq 1 \) and \( a_1 = 7 \) d) \( a_{n+1} = 6a_n \) for \( n \geq 1 \) and \( a_1 = 6 \)
Transcribed Image Text:**Problem Statement:** Give a recursive definition of the following sequences \((a_n)_{n \geq 1}\). Put the appropriate letter next to the corresponding sequence. 1. \( a_n = 6 \) 2. \( a_n = 6n + 1 \) 3. \( a_n = 6^n \) 4. \( a_n = 6n \) **Recursive Definitions:** a) \( a_{n+1} = a_n + 6 \) for \( n \geq 1 \) and \( a_1 = 6 \) b) \( a_{n+1} = a_n \) for \( n \geq 1 \) and \( a_1 = 6 \) c) \( a_{n+1} = a_n + 6 \) for \( n \geq 1 \) and \( a_1 = 7 \) d) \( a_{n+1} = 6a_n \) for \( n \geq 1 \) and \( a_1 = 6 \)
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