Geometric Sequences.notebook
Warm UP: On a separate sheet of paper...to be turned in!
April 03, 2017
Using your textbook and notes make a foldable for Unit 4 formulas
Front Unit 4 formulas: Inside Left:
1. A subway pass had a starting value of $200(a 0=100). After one ride, the value of the pass is $198.50. After two rides, its value is $197.
After 3 rides its remaining value is $195.50 Write an explicit formula to represent the remaining value on the card as an arithmetic sequences. What is the value of the pass after 15 rides?
2.You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. Write both Recursive & Explicit formulas. What is the total distance the object will fall in 6 seconds? Inside Right:
1. Exponential growth or decay (no %) Write the formula Example
2. Exponential growth (%)
3. Exponential decay (%)
Arithmetic
4. Compound interest
5. Algebraic Sequence Recursive formula
Reference pages: 269, 426, 437
6. Algebraic Sequence Explicit formula 7. Geometric Sequence Recursive formula
8. Geometric Sequence Explicit formula
Geometric Sequences
Geometric Sequence: the ratio of any term to its preceding term is a constant value.
Recursive Formula: an+1 = a n* r , for n ≥ 2
an = now term
Geometric n th Term Explicit Formula:
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an+1 = next term
r = common ratio
Problem 1: Identifying Geometric Sequences
Which of the following are geometric sequences? If geometric write the recursive formula.
a) 20, 200, 2000, 20000, 200000...
b) 2, 4, 6, 8, 10...
c) 5, ­5, 5, ­5, 5...
Now You Try: Which of the following are geometric? If not geometric, is it arithmetic? If geometric write the recursive formula.
a) 3, 6, 12, 24, 48,...
b) 3, 6, 9, 12, 15, ...
c) 1/3, 1/9, 1/27, 1/81, ...
d) 4, 7, 11, 16, 22, ...
Problem 2: Finding Recursive and Explicit Sequences
Find the recursive and explicit formulas for the sequence 7, 21, 63, 189, ...
Step 1: Identify the starting value ( a1 ).
Step 2: Find the common ratio ( r ).
Recursive Formula
Explicit Formula
a1 = ; an+1 = an r
an = a1 r n­1 Problem 3: Using Sequences
Two managers at a clothing store created sequences to show the original price and the marked­down prices of an item. Write a recursive formula and an explicit formula for each sequence. What will the price of the item be after the 6th markdown? What will be the price after the 10th markdown? (Round answers to the nearest penny.)
First Sequence
Second Sequence
$60, $51, $43.35, $36.85,...
$60, $54, $48.60, $43.74,...
Recursive
Now You Try: Find the recursive and explicit formulas for each of the following.
a) 2, 4, 8, 16, ...
Explicit
b) 40, 20, 10, 5, ...
Now You Try: Write a recursive and explicit formula for each sequence. Find the 8th term of each sequence.
a) 14, 84, 504, 3024,...
b) 648, 324, 162, 81, ...
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Geometric Sequences.notebook
April 03, 2017
Problem 4: Writing Geometric Sequences as Functions
Homework:
A geometric sequence has an initial value of 6 and a common ratio of 2. Write a function to represent the sequence. Graph the function.
Page 427 # 2­40 even, n­1
an = a1 * r Explicit Formula
Substitute f(x) for an , 6 for a1, and 2 for r.
Now find f(2), f(3), f(4), f(5) and graph the points.
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