Arithmetic Sequences and Series CHAPTER 8 2 Arithmetic

Arithmetic Sequences and Series CHAPTER 8. 2

Arithmetic Sequence An Arithmetic Sequence has a constant difference between any two consecutive terms. The Common Difference is denoted by d.

Arithmetic or not… 1. ) 7, 10, 13, 16, … 2. ) 15, 8, 1, -6, … 3. ) 8, 4, 2, 1, … 4. ) 15, 9, 3, -3, …

Arithmetic Sequence Rule: an is the n term, a 1 is the first term in the sequence, n is the number of terms, and d is where th the common difference. Note: You need the beginning number and the common difference to write a rule.

Using the Rule… Write a rule for each sequence. Ex. 1. ) 3, 8, 13, 18, … a 1 = 3, d = 5 Ex 2. ) 15, 8, 1, -6, … Find the 20 th term.

Write a rule given the common difference and a term in the sequence. Given: Find the rule for this sequence. Now use the information to write the rule.

Writing a rule given two terms Given Now we have too many unknowns. We have the 5 th term is -43. And we have the 12 th term is -8. Now we have produced 2 equations with 2 unknowns.

Now we can solve for the 2 missing variables using system of equations. d=5, now substitute 5 in for d in one of the original equations to find a 1. Now substitute d=5 and a 1 = -63 into the Arithmetic Sequence Rule formula.

Sum of an Arithmetic Sequence. ; where n is the number of terms, a 1 is the first term of the sequence, an is the last term of the sequence, and S is the sum of the sequence. n = (Top – Bottom) + 1 = (8 -1) + 1 = 7 + 1 = 8 terms First term a 1 = 2(1) - 3= -1 Last term an = 2(8) - 3= 13

Sum Continued… S= = = 8(6) = 48

HOMEWORK 5/19/16 PAGE 422 1, 2, 6 – 38 even, 44 – 58 even, 59