1 25. az = 1, an+1 =(a, +4) a) Since the sequence is recursive find an b) Find lim a,n n- DO c) If bounded, find the upper and lower bounds or explain why not if it is not bounded

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem 25**

Given:
- \( a_1 = 1 \)
- \( a_{n+1} = \frac{1}{3}(a_n + 4) \)

Tasks:
a) Since the sequence is recursive, find \( a_n \).

b) Find \( \lim_{{n \to \infty}} a_n \).

c) If bounded, find the upper and lower bounds or explain why not if it is not bounded.
Transcribed Image Text:**Problem 25** Given: - \( a_1 = 1 \) - \( a_{n+1} = \frac{1}{3}(a_n + 4) \) Tasks: a) Since the sequence is recursive, find \( a_n \). b) Find \( \lim_{{n \to \infty}} a_n \). c) If bounded, find the upper and lower bounds or explain why not if it is not bounded.
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