a. Answer Common difference makes a sequence arithmetic. Explanation Given information: A sequence Calculation: A sequence is a set of numbers, called terms, arranged in some particular order. An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. If the sequence has a common difference, it's arithmetic. For example 2,4,6,8,10 is a arithmetic sequence with common difference 2. So, common difference makes a sequence arithmetic. b. To determine To explain: what makes a sequence geometric. Answer Common ratio makes a sequence geometric Explanation Given information: A sequence Calculation: A sequence is a set of numbers, called terms, arranged in some particular order. A geometric sequence is a sequence with the ratio between two consecutive terms constant. The ratio is called the common ratio. If the sequence has a common ratio, it's geometric. For example 2,4,8,16,32 is a geometric sequence with common ratio 2. So, common ratio makes a sequence geometric.

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

Chapter 8, Problem 81CR

To determine

To explain: what makes a sequence arithmetic.

Expert Solution

Answer to Problem 81CR

Common difference makes a sequence arithmetic.

Explanation of Solution

Given information: A sequence

Calculation:

A sequence is a set of numbers, called terms, arranged in some particular order. An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference.

If the sequence has a common difference, it's arithmetic.

For example 2,4,6,8,10 is a arithmetic sequence with common difference 2.

So, common difference makes a sequence arithmetic.

To determine

To explain: what makes a sequence geometric.

Expert Solution

Answer to Problem 81CR

Common ratio makes a sequence geometric

Explanation of Solution

Given information: A sequence

Calculation:

A sequence is a set of numbers, called terms, arranged in some particular order. A geometric sequence is a sequence with the ratio between two consecutive terms constant. The ratio is called the common ratio.

If the sequence has a common ratio, it's geometric.

For example 2,4,8,16,32 is a geometric sequence with common ratio 2.

So, common ratio makes a sequence geometric.

Chapter 8, Problem 80CR

Chapter 8, Problem 82CR

Chapter 8 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Prob. 60E Ch. 8.1 - 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