12.3 Arithmetic Sequences and Series

1. 12.3 Arithmetic Sequences and Series 9.2.2.4 Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively.

2. Lesson Objective: I will be able to find terms in a arithmetic sequence and find sums of an arithmetic sequence. • What is the difference between sequence and series? Guiding Question: What does it mean for a sequence or series to be arithmetic?

3. Arithmetic Sequence: Arithmetic sequences are sequences that have a common difference. • To be arithmetic: You must add/subtract the same thing to get your sequence. • Consider these 2 sequences, which one is arithmetic • -10, -4, 2, 8, 14 • -2, -5, -11, -20, -32 Guiding Question: What does it mean for a sequence or series to be arithmetic?

4. To find a specific term This is the algebraic rule. Ex. Find the 12th term of this sequence. {-3, -5, -7, -9…} Guiding Question: What does it mean for a sequence or series to be arithmetic?

5. I can also use it to fill in missing terms in a sequence. 17, __, __, __, -7. 2, __, __, __, -22 • Substitute in for the given parts (, , ) • Find your common difference • Find the missing terms Guiding Question: What does it mean for a sequence or series to be arithmetic?

6. You can also use given any 2 terms in a sequence. 2. , find the 4th term. • 1. , find the 5th term Find the common difference Find the 1st term Find the term you want. Guiding Question: What does it mean for a sequence or series to be arithmetic?

7. Guiding Question: What does it mean for a sequence or series to be arithmetic? For a series to you have to add n terms. The sum of the 1st n terms of an arithmetic series can be found by this formula

8. Find the indicated sum • Find this sum 1. Guiding Question: What does it mean for a sequence or series to be arithmetic?

9. Assignment Pg. 884 21-35 • Day 2 Pg. 885 36, 43-46, 52-57 Guiding Question: What does it mean for a sequence or series to be arithmetic?