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Date 
Entry Task 
Activity 
Assignments and Homework* 
4/13 
Work in your table groups to determine the
next five numbers in the sequences. {4, 4, 8, 12, 20, 32, ... } {1, 2, 3, 4, 5, 6, ... } {0000, 0001, 0010, 0011, 0100, ...}. Additional Resources:

Intro to discrete mathematics.
Notes from Today's Class 
Give the first four terms and the 31st term
of the following sequences:
Today's Goals: Students will become familiar with the differences between sequences and series, learn about notation and both explicit/recursive formulas. 
4/14 
Determine the first five terms of the
following sequence:a_{1} = 1 
History of the
Fibonacci Sequence Recursively Defined Sequences. Finding a Pattern activity. JR: Lucas numbers are developed similarly to Fibonacci numbers. Determine the first 10 numbers in the sequence. 
Complete Finding
a Pattern activity. 1) Determine the first 10 terms of this sequence and graph your results (on paper): a_{1} = 12) Determine the nth term (formula) of this sequence (the first term given is when n = 1): Test Corrections: Today (4/14)PM, Tomorrow (4/15)AM Today's Goals: Students will recognize patterns of various sequences and will define them recursively. 
4/15 
Recall the sequence assigned for homework
on 4/1 {1/0!, 1/1!, 1/2!, 1/3!, 1/4!, ...,}: Write a formula for the n^{th} term of the sequence. 
Partial Sums & Sigma Notation. Using the Notation
activity. The Harmonic Series Activity JR: Identify and explain in simple language each component of sigma notation. 
1. Compute the sum of 2. Write the sum of the following using sigma notation: Test Corrections: Today AM Today's Goals: Students will practice using converting a sum to sigma notation and computing sums using notation for partial sums. Introduction to infinite sums. 
4/17 
Label each of the following as either a
geometric or arithmetic sequence and explain your
reasoning

Made In The
Shade activity. JR: Explain in simple terms how to construct a sequence that represents the area of the shaded regions from today's activity. Solutions to Made In The Shade 
1. When an object is allowed to fall freely
near the surface of the earth, the gravitational pull is
such that the object falls 16 feet in the first second, 48
feet in the next second, 80 feet in the next second and so
on.
2. A biologist is trying to find the optimal salt
concentrations for the growth of a certain species of
mollusk. She begins with a brine solution that has 4g/L
of salt and increases the concentration by 10% every
day. Let C_{0} denote the initial concentration
and C_{n} the concentration after n days.

4/20 
An architect designs a theater with 15
seats in the first row, 18 in the second row, 21 in the
third row, etc. If the theater must seat 870, how
many rows must there be?

Practice with Quiz Topics. JR: In the wellknown song "The Twelve Days of Christmas," a person gives his sweetheart k gifts on the k^{th} day for each of the 12 days of Christmas. The person also repeats each gift identically on each subsequent day. Thus, on the 12th day, the sweetheart receives a gift for the first day, 2 gifts for the second, 3 gifts for the third, and so on. Setup a sum with Sigma notation that will model the total number of gifts received up to day k. 
Prepare for the Quiz tomorrow. 1) Write an explicit formula for the following sequence. {0, 2, 4, 6, 8, 10, 12, ...}2) Write a recursive formula for the sequence above. 3) Use sigma notation to write the sum of the first 8 terms of the sequence above. 4) Calculate the sum from question 3. Today's Goals: Review challenging concepts and prepare for the unit assessment. 
4/21 
Get ready for the quiz!

Unit Quiz 9.1

