School Improvement in Maryland

Using the State Curriculum: Mathematics, Grade 8

Algebra | 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 teacher-not 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


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 8th term of the sequence: 3, 6, 12, 24, ...

Answer: 384

To determine the common ratio find 6/3 or 12/6 or 24/12 = 2.

Multiply each successive term by 2 until you get to the 8th term, 384.

Classroom Example 2

What is the value of x in the table?

1 2 3 4 5
7500 1500 300 60 x

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 1/5 because 1500/7500 = 1/5. Each term is 1/5 of the previous term, so the answer should be 1/5 of 60, or 12.

Resources for Objective 1.A.1.b:
CLARIFICATIONS | Lesson Seeds | Sample Assessments |