Using the State Curriculum: Mathematics, Grade 8Algebra  Geometry  Measurement  Statistics  Probability  Number  Processes 
Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teachernot the student. In addition, classroom examples may or may not reflect the assessment limits. 
Standard 1.0 Knowledge of Algebra, Patterns, and Functions 
Topic A. Patterns and Functions 
Indicator 1. Identify, describe, extend, and create patterns, functions and sequences 
Objective b. Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph 
Clarification 


A sequence is an ordered set of related numbers. This relationship is expressed recursively when each number in the sequence is determined using the previous number, or term. Members of the set of numbers in the sequence are called terms. A geometric sequence is an ordered set of numbers in which each member in the set is determined by multiplying the preceding term by a constant value. This constant value is the ratio of the second term to the first term or the ratio of third term to the second term, etc. 

Classroom Example 1 

Determine the 8^{th} term of the sequence: 3, 6, 12, 24, ... Answer: 384 To determine the common ratio find . Multiply each successive term by 2 until you get to the 8^{th} term, 384. 

Classroom Example 2 

What is the value of x in the table?
Answer: 12 Use what you know about recursive relationships of geometric sequences to justify why your answer is correct. Use words, numbers, and/or symbols in your justification. Sample correct response: The constant ratio is because . Each term is of the previous term, so the answer should be of 60, or 12. 

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