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Lesson Seeds: The lesson seeds are ideas for the indicator/objective that can be used to build a lesson. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction.

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

Assessment limit: Provide the nth term no more than 5 terms beyond the last given term using the recursive relationship of geometric sequences with whole numbers and a common ratio of no more than 5:1 (0 – 10,000)

Materials needed

Sets of index cards, each set containing out-of-order cards with the terms of a geometric sequence.

Activities
  • Students will work in groups to order terms and determine the recursive rule for a geometric sequence. Provide each group with a set of index cards containing the terms of the sequence.
  • With students working in groups, tell students that there is a relationship among these terms, and ask them to put them in the order that creates a pattern.
  • The students must present their sequence to the class and explain the relationship.
  • From this activity, develop the definitions of geometric sequence, common ratio, and recursive relationship. Be prepared for students to put terms in ascending or descending order, and discuss the difference of the common ratio when this occurs.

Geometric Sequence — an ordered set of numbers in which a number in the set is determined by multiplying the previous term by a constant value, or common ratio.

Common Ratio — the ratio formed by the ratio of two consecutive terms in a geometric sequence. The common ratio can be found by dividing a term in the sequence by the preceding term.

Recursive Relationship — Each term, or number, in the sequence is calculated using the previous term in the sequence.

An example of a geometric sequence is 2, 6, 18, 54, . . . The common ratio is 3 because 6/2, 18/6, and 54/18 all equal 3. This sequence is a recursive relationship because each term is determined by multiplying the previous term by 3.

Another example of a geometric sequence is 54, 18, 6, 2, . . . The common ratio is 1/4 because 18/54 , 6/18 , and 2/6 all equal 1/4.
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Resources for Objective 1.A.1.b:
Clarifications | LESSON SEEDS | Sample Assessments |