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Math patterns 2
Description
Exercise Name: Math patterns 2
Math Missions: 4th grade (U.S.) Math Mission, Pre-algebra Math Mission, Mathematics I Math Mission
Types of Problems: 3

The Math patterns 2 exercise appears under the 4th grade (U.S.) Math Mission, Pre-algebra Math Mission and Mathematics I Math Mission. This exercise introduces the idea of arithmetic sequences as recognition of a repeating pattern.

## Types of Problems

There are three types of problems in this exercise:

1. Fill in the arithmetic sequence: This problem provides a chart that begins with a number and follows a pattern of adding the same number over and over. The user is asked to fill in the chart completely to get to a particular value.
2. Extend pattern into the future: This problem involves a cyclic pattern that continues indefinitely. Users are asked to use the pattern to predict a future event.
3. Select all that apply about the pattern: This problem describes an arithmetic sequence. It has several statements about a particular term or pattern in the sequence and the user is asked to select all statements that are true.

## Strategies

The properties of arithmetic sequences are not needed to accomplish this problem, but would possibly help. The properties of cyclical results can be used in many other venues such as the last digit of numbers raised to powers and even the powers of the imaginary unit.

1. The explicit formula for the nth term of an arithmetic sequence is ${a_n=a_1+(n-1)d}$ when ${a_1}$ is the first term of the sequence, ${d}$ is the common difference, and n is the number of the term desired. This is not necessary knowledge, but can be used.
2. Often times writing out a few terms of a sequence can give insight into properties that may be true of all members of the sequence.

## Real-life applications

1. Pattern recognition is a common skill on IQ tests.