3 4 Arithmetic Sequences Sequence a set of

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 #1 A & 1 B

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, a 1, a 2, …, can be found as follows: a 1, a 2 = a 1 + d, a 3 = a 2 + d, a 4 = a 3 + d, … Where d is the common difference, a 1 is the first term, a 2 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 a 1 and the common difference d. Term Symbol In Terms of a 1 and d Numbers First a 1 8 Second a 2 a 1 + d 8 + 3 = 11 Third a 3 a 1 + 2 d 8 + 2(3) = 14 Fourth a 4 a 1 + 3 d 8 + 3(3) = 17 nth term an a 1 + (n-1)d 8 + (n-1)(3) This leads to the formula that can be used to find any term in an arithmetic sequence: a 1 + (n-1)d, where an is the nth term, a 1 is the first term, and d is the common difference. N must be a positive integer.

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

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