Sequences & Series: Arithmetic, Geometric, Infinite! Chapter 11 REVIEW Sequences & Series: Arithmetic, Geometric, Infinite!

Arithmetic Sequences Example: Write the explicit arithmetic rule. 2, 5, 8, 11, 14, … nth term 1st term common difference

Arithmetic Series Example: Find the sum of the first 20 terms. 2 + 5 + 8 + 11 + 14 + … 1st term nth term

Geometric Sequences Example: Write the explicit geometric rule. 2, -6, 18, -54, 162, … 1st term common ratio

Geometric Series Example: Find the sum of the first 10 terms. 2 - 6 + 18 - 54 + 162 … 1st term!!!

Infinite ∞ Geometric Series! Example: Find the sum. 64 + 32 + 16 + 8 + … but only if |r|<1

Summation Notation Let’s try it! … means that we start with the first term and add all the way to the 7th term! Let’s try it!

Recursive Rules Example: Write the recursive rule. 2, 5, 10, 50, 500, … Arithmetic Geometric

Example MC Questions Which of the following expresses the series 3 + 9 + 27 + 81 in summation notation? A) B) C) D) E)

Example MC Questions Write the explicit formula for the nth term of the arithmetic sequence with a4 = 7 and a13 = 34. A) 3n – 2 B) 3n – 5 C) 3n + 2 D) 3n + 5 E) none of these

Example MC Questions Write the explicit formula for the nth term of the geometric sequence with a5 = 48 and r = 2. A) 2n B) 2(3)n C) 2(3)n D) 3(2)n-1 E) 3(2)n-1

Example MC Questions Which of the following gives the first 11 terms of the geometric series 5 + 10 + 20 + 40 + … A) B) C) D) E)