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Determine the explicit formula for the following sequences. 4. Sequence: }, ,7, 3, 4, ... a, = } and d=

Determine the explicit formula for the following sequences. 4. Sequence: }, ,7, 3, 4, ... a, = } and d=

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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## Determine the Explicit Formula for the Following Sequences **4. Sequence:** \[ \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \frac{11}{6}, \ldots \] - **Starting Term (\(a_1\)):** \(\frac{1}{2}\) - **Common Difference (\(d\)):** \(\frac{1}{3}\) **Explicit Formula:** \[ a_n = a_1 + (n-1) \cdot d \] Substitute \(a_1 = \frac{1}{2}\) and \(d = \frac{1}{3}\) into the formula to determine \(a_n\).
Transcribed Image Text:## Determine the Explicit Formula for the Following Sequences **4. Sequence:** \[ \frac{1}{2}, \frac{5}{6}, \frac{7}{6}, \frac{3}{2}, \frac{11}{6}, \ldots \] - **Starting Term (\(a_1\)):** \(\frac{1}{2}\) - **Common Difference (\(d\)):** \(\frac{1}{3}\) **Explicit Formula:** \[ a_n = a_1 + (n-1) \cdot d \] Substitute \(a_1 = \frac{1}{2}\) and \(d = \frac{1}{3}\) into the formula to determine \(a_n\).
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