1. Algebra Rules!-Part 1

2. Operating With Sequences
Four sequences are shown below.

3. The four patterns are different
The four patterns are different. What do you notice the patterns have in common? How many squares, dots, stars, or bars will the 100th figure in each sequence have? Explain how you know. The numbers in a sequence form an arithmetic sequence if they have equal increases or decreases from term to term. The numbers in a sequence form a geometric sequence if the next term is found by multiplying the previous term by a non-zero constant.

4. Arithmetic Sequences
The diagram to the left represents an arithmetic sequence. Notice, the steps have an equal increase from step to step. The expression that represents this arithmetic sequence is found in the green box. Sequences are in the form a+bn, where ‘a’ is the starting term, ‘b’ is the constant, and ‘n’ is the number of the term in the sequence.

5. Examples:

6. You can also add or subtract arithmetic sequences to get a new sequence.

7. Write an expression for the sum of 12 + 10n and 8 - 3n
Write an expression for the sum of n and 8 - 3n. Write an expression for the sum of n and 11 – 9n

8. Fill In the missing Numbers and Expressions:

9. Rewrite the expression as short as possible: (2+n)+(1+n)+n+(-1+n)+(-2+n)

11. Find the missing expression: (6+4n) – (8+3n)