2. Aim: Geometric Sequence Course: Math Literacy Do Now: Aim: What are geometric sequences? Mrs. Gonzales sells houses and makes a commission of $3750 for the first house sold. She will receive a $500 increase in commission for each additional house sold. How many houses must she sell to reach total commissions of $65000?

3. Aim: Geometric Sequence Course: Math Literacy Model Problem Mrs. Gonzales sells houses and makes a commission of $3750 for the first house sold. She will receive a $500 increase in commission for each additional house sold. How many houses must she sell to reach total commissions of $65000? S n = 65000a 1 = 3750d = 500 a n = a 1 + (n – 1)d n = 10.58 and –24.58 She must sell 11 houses.

4. Aim: Geometric Sequence Course: Math Literacy Geometric Sequence Determine the next three terms in the following sequences 1, 2, 4, 8,... 0.1, 1, 10, 100,... 336, 168, 84, 42,... 900, 300, 100,...

5. Aim: Geometric Sequence Course: Math Literacy 2, 4, 8, 16,...., 12, 36, 108, 324,....r = 3 r = 2 Definition of Geometric Sequence A sequence is geometric if the ratios of consecutive terms are the same. Sequence a 1, a 2, a 3, a 4,..... a n,... is geometric if there is a number r, r  0, such that and so on. The number r is the common ratio of the geometric sequence. r = ? n th ? r = -1/3 2 n,... 4(3) n,...

6. Aim: Geometric Sequence Course: Math Literacy The n th term of an geometric sequence has the form where r is the common ratio between consecutive terms of the sequence. Thus ever geometric sequence can be written in the following form The n th Term of a Geometric Sequence a 1 a 2 a 3 a 4..... a n.... a 1 a 1 r a 1 r 2 a 1 r 3.... a n = a 1 r n – 1, a 1 r n - 1.... recursive definition:a n = a n – 1 · r

7. Aim: Geometric Sequence Course: Math Literacy n th Term of a Geometric Sequence Find the first five terms of the geometric sequence whose first term is a 1 = 3 and whose common ratio is r = 2. a n = a 1 r n – 1 a 1 = a 1 r 1 – 1 a 2 = a 1 r 2 – 1 a 3 = a 1 r 3 – 1 a 4 = a 1 r 4 – 1 a 5 = a 1 r 5 – 1 = 3(2) 0 = 3(2) 1 = 3(2) 2 = 3(2) 3 = 3(2) 4 = 3 = 6 = 12 = 24 = 48

8. Aim: Geometric Sequence Course: Math Literacy Finding a Term Find the 12 th term of the geometric sequence 5, 15, 45,... a n = a 1 r n – 1 a 12 = 5(3) 11 = 885,735 r = 15/5 = 3 Find the 15 th term of the geometric sequence whose first term is 20 and whose common ratio is 1.05. a n = a 1 r n – 1 a 15 = 20(1.05) 14  39.599 r = 1.05 The 4 th term of a geo. sequence is 125, and the 10 th is 125/64. Find the 14 th. 4 th term times r 6 = 10 th term or a 10 = a 4 r 6 Consider the 4 th term as if it were the 1 st term

9. Aim: Geometric Sequence Course: Math Literacy Model Problem A company purchases $50,000 worth of copiers on Jan. 1, 1996. This asset depreciates at a rate of 45% per year. What is the value of this asset at the end of 2001 (or 1/1/02)? a n = a 1 r n – 1, (note: a 45% depreciation rate means the asset retains 55% of its value) a 1 = 50,000r =.55n = 2002... 1996 = 7 a 7 = 50000(.55) 7-1 a 7  1384.032031 Asset is worth approximately $1384.03

10. Aim: Geometric Sequence Course: Math Literacy Model Problem You want to a reduced copy of a photo. The actual length of the photo is 10 in. The smallest size the copier can make is 64% of the original. Find the length of the photo after five reduction at 64%. a n = a 1 r n – 1 a 1 = 10r =.64n = 6 a 6 = 10(.64) 6-1 a 6  1.07 After reduction the photo is about 1 in. long.