3-4: Arithmetic Sequences

Sequence: a set of numbers in a specific order Terms: the numbers in a sequence Arithmetic Sequence: numerical pattern that increases or decreases at a constant rate or value Common Difference: the constant difference between the terms

Identify Arithmetic Sequences Determine whether each sequence is arithmetic. Explain. 1, 2, 4, 8, … No, because the difference between terms is not constant. ½, ¼, 0, -1/4, … Yes, because the difference between terms is constant Check Your Progress #1A & 1B

Writing Arithmetic Sequences Each term of an arithmetic sequence after the first term can be found by adding the common difference to the preceding term. An arithmetic sequence, a1, a2, …, can be found as follows: a1, a2 = a1 + d, a3 = a2 + d, a4 = a3 + d, … Where d is the common difference, a1 is the first term, a2 is the second term, and so on.

Writing Arithmetic Sequences The arithmetic sequence 66, 60, 54, 48, … represents the amount of money that John needs to save at the end of each week in order to buy a new game. Find the next three terms. Find the common difference by subtracting the successive terms. The common difference is -6 Add -6 to the last term of the sequence to get the next term. Continue adding -6 until the next three terms are found. 48 – 6 = 42, 42 – 6 = 36, 36 – 6 = 30

Check Your Progress #2

Each term in an arithmetic sequence can be expressed in terms of the first term a1 and the common difference d. This leads to the formula that can be used to find any term in an arithmetic sequence: a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference. N must be a positive integer. Term Symbol In Terms of a1 and d Numbers First a1 8 Second a2 a1 + d 8 + 3 = 11 Third a3 a1 + 2d 8 + 2(3) = 14 Fourth a4 a1 + 3d 8 + 3(3) = 17 nth term an a1 + (n-1)d 8 + (n-1)(3)

Example 3 Page 167 Check Your Progress #3A, 3B, & 3C

Homework Assignment #24 Page 168 #12-38 even, 40-45, 50-52