The document discusses arithmetic sequences, which are patterns of numbers where each term is found by adding a constant to the previous term. This constant is called the common difference. Examples of arithmetic sequences and their common differences are provided, along with explanations of how to find patterns in sequences and calculate specific terms. Formulas for writing equations of arithmetic sequences and finding terms are also outlined.

1. What comes next?3, 5, 7, 9, __, __, __An arithmeticsequence is a pattern of numbers in which each number is found by adding a constant to the number before it.11 13 15+2+2+2+2+2+2Common differenced = 2a1 = 3a2 = 5a3 = 7

2. What’s the common difference?8, 10.5, 13, 15.5, …d = 2.59, 5, 1, -3, …d = -4

3. 3, 5, 7, 9, 11, 13, 15, …+2+2+2a1 = 3a2 = 5 3 + 1(2)a3 = 7 3 + 2(2)a4 = 9 3 + 3(2) an = a1 + (n – 1)d

4. Write an equation for the nth term of the arithmetic sequence –8, –6, –4, ….Find the 80th term of the sequence a80 = 2(80) – 10 = 160 – 10 = 150Example 1-3a

5. Complete the statement for the arithmetic sequence:124 is the ____ term of -2, 5, 12, …-27124124 = -2 + 7n – 7124 = 7n – 9 133 = 7n19 = n

6. The terms between any two nonconsecutive terms of an arithmetic sequence are arithmetic means.Find the three arithmetic means between 21 and 45.21, ___, ___, ___, 45, ...,Example 1-4a

7. The terms between any two nonconsecutive terms of an arithmetic sequence are arithmetic means.Find the three arithmetic means between 21 and 45.21, ___, ___, ___, 45, ...,+d+d+d+dExample 1-4a

8. The terms between any two nonconsecutive terms of an arithmetic sequence are arithmetic means.Find the three arithmetic means between 21 and 45.21, ___, ___, ___, 45, ...,+d+d+d+dExample 1-4a

9. The terms between any two nonconsecutive terms of an arithmetic sequence are arithmetic means.Find the three arithmetic means between 21 and 45. 27 33 3921, ___, ___, ___, 45, ...,+d+d+d+dExample 1-4a