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Given 8₂ = 6 and 85 = -384 of a geometric sequence, what is the recursive equation for the nth term?

Given 8₂ = 6 and 85 = -384 of a geometric sequence, what is the recursive equation for the nth term?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Recursive Equations for a Geometric Sequence** Given \(a_2 = 6\) and \(a_5 = -384\) of a geometric sequence, what is the recursive equation for the \(n\)th term? 1. \(a_n = -4(a_{n-1}), \; a_1 = -1.5\) 2. \(a_n = -4(a_{n-1}), \; a_1 = 1.5\) 3. \(a_n = 4(a_{n-1}), \; a_1 = -1.5\) 4. \(a_n = 4(a_{n-1}), \; a_1 = 1.5\) **Explanation:** Each option represents a possible recursive equation for the geometric sequence, where each term is generated by multiplying the previous term by a constant ratio. The initial term (\(a_1\)) is also given for each option. This setup helps to determine the correct recursive equation by matching the given conditions of the sequence.
Transcribed Image Text:**Recursive Equations for a Geometric Sequence** Given \(a_2 = 6\) and \(a_5 = -384\) of a geometric sequence, what is the recursive equation for the \(n\)th term? 1. \(a_n = -4(a_{n-1}), \; a_1 = -1.5\) 2. \(a_n = -4(a_{n-1}), \; a_1 = 1.5\) 3. \(a_n = 4(a_{n-1}), \; a_1 = -1.5\) 4. \(a_n = 4(a_{n-1}), \; a_1 = 1.5\) **Explanation:** Each option represents a possible recursive equation for the geometric sequence, where each term is generated by multiplying the previous term by a constant ratio. The initial term (\(a_1\)) is also given for each option. This setup helps to determine the correct recursive equation by matching the given conditions of the sequence.
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