**FINITE MATHEMATICS**

*Competency 209.1.1: Discrete Mathematics –**The graduate applies the fundamental ideas of discrete mathematics including logic, set theory, and graph theory in formulating and solving problems.*

**Task 6: Number Patterns**

**Introduction:**

Mathematics is sometimes described as “the science of patterns.” Two fundamental patterns are arithmetic and geometric sequences. It is important to know how to represent these patterns with simple algorithms and precise algebra.

**Requirements:**

*Your submission must be your original work. No more than a combined total of 30% of the submission and no more than a 10% match to any one individual source can be directly quoted or closely paraphrased from sources, even if cited correctly. Use the Turnitin Originality Report available in Taskstream as a guide for this measure of originality.*

*You must use the rubric to direct the creation of your submission because it provides detailed criteria that will be used to evaluate your work. Each requirement below may be evaluated by more than one rubric aspect. The rubric aspect titles may contain hyperlinks to relevant portions of the course.*

A. Provide the first **five** terms of an arithmetic or geometric sequence that has a first term higher than 10 and a common difference or ratio that is positive but not 1.

1. Explain how to determine the *n*th term formula.

2. Find the 30th term, showing all work.

B. Explain how to use patterns or sequences to determine the last digit of the number 7^{N}, where N is the four-digit year of your birth.(N is 1988)

C.

Acknowledge sources, using APA-formatted in-text citations and

references, for content that is quoted, paraphrased, or summarized.

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