12.2: Arithmetic Sequences Worksheet Key 17)` 1010 18) 6950 19) 9925 20) 3080 21) 63 22) -1435 23) 10875 24) -4750 25) 7 2/15/2019 9:48 PM 12.2: Arithmetic Sequences

Geometric Sequences & Series Section 12.5 Pre–Calculus, Revised ©2015 2/15/2019 9:48 PM 12.1: Sequences

Definitions Geometric Sequence is where consecutive terms have a common ratio Geometric Series is indicated sum of the terms of a geometric sequence Ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another 2/15/2019 9:48 PM 12.1: Sequences

Is it Geometric? YES r = 3 NO YES r = 0.2 Determine whether these sequences are geometric. If it is, determine the ratio. 1, 3, 9, 27, 81... 180, 90, 60, 15, 3.75 ... 5, 1, 0.2, 0.04, 0.008 ... –50, –32, –18, –8, –2 ... YES r = 3 NO YES r = 0.2 2/15/2019 9:48 PM 12.1: Sequences

Steps Find the common ratio Use the formula and determine the rule Evaluate for the missing variable 2/15/2019 9:48 PM 12.1: Sequences

Example 1 For this geometric sequence, determine the first four terms of 𝒂 𝒏 =𝟓 𝟐 𝒏−𝟏 n 5(2)n–1 an 1 2 3 4 1 5(2)1–1 5 2 5(2)2–1 10 3 5(2)3–1 20 4 5(2)4–1 40 2/15/2019 9:48 PM 12.1: Sequences

Example 2 For this geometric sequence, determine the first four terms of 𝒂 𝒏 =𝟓 𝟏 𝟖 𝒏−𝟏 2/15/2019 9:48 PM 12.1: Sequences

Example 3 Find the 7th term of this geometric sequence of 1, 3, 9, 27, 81... and the explicit rule n an 1 2 3 9 4 27 5 81 2/15/2019 9:48 PM 12.1: Sequences

Your Turn Find the 8th term of this geometric sequence of 16, –8, 4, –2, .... and the explicit rule 2/15/2019 9:48 PM 12.1: Sequences

Example 4 Find the 8th term of the geometric sequence with a3 = 36 and a5 = 324. 2/15/2019 9:48 PM 12.1: Sequences

Example 4 Find the 8th term of the geometric sequence with a3 = 36 and a5 = 324. 2/15/2019 9:48 PM 12.1: Sequences

Your Turn Find the 8th term of the geometric sequence with a2 = 80 and a4 = 1280 2/15/2019 9:48 PM 12.1: Sequences

Geometric Series Identify the number of terms, lower and upper limit, and common ratio of the summation Then, identify the missing terms by plugging the given equation Apply the geometric summation notation equation, 𝒌=𝟏 𝒏 𝒂 𝒌 𝒓 𝒏 = 𝒂 𝟏 𝟏− 𝒓 𝒏 𝟏−𝒓 where ak is the given equation, a1 is the given term, and an is the last term 2/15/2019 9:48 PM 12.1: Sequences

Example 5 Find the indicated sum for the geometric series of s8 = 1 + 2 + 4 + 8… 2/15/2019 9:48 PM 12.1: Sequences

Example 6 Evaluate 𝒌=𝟏 𝟏𝟎 𝟐 𝒌 2/15/2019 9:48 PM 12.1: Sequences

Your Turn Find the indicated sum for the geometric series of s9 = –3 + –6 + –12… 2/15/2019 9:48 PM 12.1: Sequences