Concept explainers
To compare and contrast arithmetic and geometric sequences.
Explanation of Solution
Given:
The arithmetic and geometric sequences.
Calculation:
Compare
The arithmetic sequence is a sequence of terms, whose differences of successive terms is constant.
The general term of the arithmetic sequence having first term
The sum of first terms of arithmetic sequence having first term
The geometric sequence is sequence of terms, whose ratio of successive terms is constant
The general term of the geometric sequence having first term
The sum of first terms of geometric series is
In Arithmetic sequence the terms are continuously positive or negative, but in the case of geometric sequence the terms are either positive or negative or alternatively positive and negative
The sum of infinite arithmetic sequence is not finite, but the sum of infinite geometric sequence whose common ration less than 1 is finite
The general term of the arithmetic sequence is linear, general term of geometric sequence is exponential.
Chapter 12 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
University Calculus: Early Transcendentals (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
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Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
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