Math patterns 2

The topic  is a topic under the 4th Grade 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 student is asked to fill in the chart completely to get to a particular value.Mp2-1.png
 * 2) Extend pattern into the future: This problem involves a cyclic pattern that continues indefinitely. The student is asked to use the pattern to predict a future event.Mp2-2.png
 * 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 student is asked to select all statements that are true.Mp2-3.png

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 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 members of the sequence.