Aim: Geometric Sequence Course: Math Literacy Do Now: Aim: What are geometric sequences? You want to a reduced copy of a photo. The actual length of the.

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Presentation transcript:

Aim: Geometric Sequence Course: Math Literacy Do Now: Aim: What are geometric sequences? 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%.

Aim: Geometric Sequence Course: Math Literacy Do Now 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.

Aim: Geometric Sequence Course: Math Literacy Find the sum of the first eight terms of the geometric sequence 1, 3, 9, 27,... The Sum of a Finite Geometric Sequence r = ?3 a 1 a 2 a 3 a a n.... a 1 a 1 r a 1 r 2 a 1 r a 1 r n (3) (3) 7 = 3280 = 1 + 1(3) + 1(3) 2 + 1(3) = 3280 Is there an easier way to find the sum of a geometric sequence?

Aim: Geometric Sequence Course: Math Literacy Find the sum of the first eight terms of the geometric sequence 1, 3, 9, 27,... previous problem The Sum of a Finite Geometric Sequence The sum of the finite geometric sequence a 1, a 1 r 2, a 1 r 3, a 1 r 4,.... a 1 r n with common ratio r  1 is given by

Aim: Geometric Sequence Course: Math Literacy Find the sum of Model Problem a 1 = 10; r = -1/2 How many terms in the series? starting at i = 0, there are 11 terms ; n = 11

Aim: Geometric Sequence Course: Math Literacy Model Problems In March, the Floyd family starts saving for a vacation at the end of August. The Floyds expect the vacation to cost $1375. The start with $125. Each month they plan to deposit 20% more than the previous month. Will they have enough money for their trip? a 1 =125r =1.20n =6 Not enough!

Aim: Geometric Sequence Course: Math Literacy Model Problems Find the sum of the series , n = 6

Aim: Geometric Sequence Course: Math Literacy Model Problems Find the sum of the geometric series.

Aim: Geometric Sequence Course: Math Literacy Model Problems Find a 1. S n = -55, r = -2/3, n = 5

Aim: Geometric Sequence Course: Math Literacy Model Problems