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Problem 1: Suppose a sequence is defined recursively by: b2 = 23 and Vn e Z where n > 3, b, = bn-1–7. Write the terms b3, b4, bg and use this information to determine a closed formula for the sequence for all nonnegative integers (that is, a formula where b, is defined by n alone with no reference to previous terms). Explicitly show that the formula you find fits the recurrence relation given (show that for the sequence you've written, the recurrence relation is true).

Problem 1: Suppose a sequence is defined recursively by: b2 = 23 and Vn e Z where n > 3, b, = bn-1–7. Write the terms b3, b4, bg and use this information to determine a closed formula for the sequence for all nonnegative integers (that is, a formula where b, is defined by n alone with no reference to previous terms). Explicitly show that the formula you find fits the recurrence relation given (show that for the sequence you've written, the recurrence relation is true).

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 1:** Suppose a sequence is defined recursively by: \( b_2 = 23 \) and \(\forall n \in \mathbb{Z} \text{ where } n \geq 3, \, b_n = b_{n-1} - 7 \). Write the terms \( b_3, b_4, b_5 \) and use this information to determine a closed formula for the sequence for all nonnegative integers (that is, a formula where \( b_n \) is defined by \( n \) alone with no reference to previous terms). Explicitly show that the formula you find fits the recurrence relation given (show that for the sequence you've written, the recurrence relation is true).
Transcribed Image Text:**Problem 1:** Suppose a sequence is defined recursively by: \( b_2 = 23 \) and \(\forall n \in \mathbb{Z} \text{ where } n \geq 3, \, b_n = b_{n-1} - 7 \). Write the terms \( b_3, b_4, b_5 \) and use this information to determine a closed formula for the sequence for all nonnegative integers (that is, a formula where \( b_n \) is defined by \( n \) alone with no reference to previous terms). Explicitly show that the formula you find fits the recurrence relation given (show that for the sequence you've written, the recurrence relation is true).
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