Knight’s Charge 8/26/15

Solve: 1)

2)

3)

Review

Have your homework out on your desk (including your triangle).

Textbooks Write your name in your textbook in the appropriate

place on the inside front cover. Fill out your index card as follows:

Turn in your index card. Remember: These books cost around $108, so

TAKE CARE OF THEM. You need to COVER YOUR BOOK!!

Student NameGlencoe Precalculus BookBook #:___________Book Condition: NEW

Check Homework 8/26/15

Set D Practice Wkst

Sequences and Series

Unit 1

Consider this:

Intro to Sequences

A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on, until there are 200 logs in the bottom row.

A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on, until there are 200 logs in the bottom row.

Intro to Sequences

Write and interpret the first 10 terms of the sequence of numbers generated from the example.

Identify the pattern in the sequence of numbers.

Write the formula for the nth term of the sequence and use it to find the number of logs in, say, the 76th row

Compute the number of logs in the first 12 rows combined.

What is the total number of logs in the pyramid?

Intro to Arithmetic Series:One of the most famous legends in the lore of mathematics concerns German mathematician Carl Friedrich Gauss. One version of the story has it that in primary school

after the young Gauss misbehaved, his teacher, J.G. Büttner, gave him a task: add the numbers from 1 to100. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant, Martin Bartels. Can you?

Gauss's realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050.

Arithmetic Series

Notation Consider the sequence:

General Sequences

the term number (think of it as the term’s place in line) the nth term

represents the FIRST term. represents the SECOND term. represents the THIRD term. represents the FOURTH term, etc…

the previous term the next term

IMPLICIT FORMULA: requires knowing the previous term

EXPLICIT FORMULA: requires only knowing the desired n.

Fill in the chart.

General Sequences

SEQUENCE IMPLICIT FORMULA

EXPLICIT FORMULA

Find the first six terms for each sequence:

,

Arithmetic, Geometric, or Neither? An arithmetic sequence is one where a constant

value is added to each term to get the next term.example: {5, 7, 9, 11, …}

A geometric sequence is one where a constant value is multiplied by each term to get the next term.

example: {5, 10, 20, 40, …} EXAMPLE: Determine whether each of the following

sequences is arithmetic, geometric, or neither:a. b. {9, -1, -11, -21, ...}c. {0, 1, 1, 2, 3, 5, 8, 13, 21,...}

GEOMETRIC

ARITHMETICNEITHER

Fibonacci Sequence

Formal Definition of an Arithmetic Sequence

Arithmetic Sequences

A sequence is arithmetic if there exists a number d, called the common difference, such that for for .

In other words, if we start with a particular first term, and then add the same number successively, we obtain an arithmetic sequence.

Example: Write an explicit formula for the sequence {10, 15, 20, 25, …}.

Arithmetic Sequences

Note: this sequence is arithmetic with a common difference (d) of 5.

Make a table of values for the terms of the sequence. Then graph the table. What do you notice

about the graph?It’s LINEAR……

Can you write the equation of the line/sequence now?Yes, the equation of the line is …

So the formula for the sequence is .

Example: Write an explicit formula for the sequence {10, 15, 20, 25, …}.

Arithmetic Sequences

So how could we write the formula WITHOUT having to graph it?

In general, the explicit formula for an arithmetic sequence is given by .

Example: Fill in the chart for each arithmetic sequence shown.

Arithmetic Sequences

SEQUENCE IMPLICIT FORMULA

EXPLICIT FORMULA 100th term

Example: Given and , find the 100th term of the sequence.

Arithmetic Sequences

Example: Given and , find the 25th term of the sequence.

Arithmetic Sequences

Arithmetic Means Example: Form an arithmetic sequence that

has 3 arithmetic means between 15 and 35.

Example: Form an arithmetic sequence that has 4 arithmetic means between 13 and 15.

Arithmetic SERIES What is an arithmetic SERIES? --the SUM

of an indicated number of terms of a sequence.

Arithmetic Sequence: Arithmetic Series:

Sum of a FINITE Arithmetic Sequence The sum of a finite arithmetic sequence with

common difference d is .

Example: Find the sum of the first 15 terms of the sequence .

Example: Find the sum of the first 100 terms of the sequence {-18, -13, -8, -3, 2,…}.

Arithmetic Series

Example: Given the sum of the first 20 terms of a sequence that starts with 5 is 220, find the 20th term.

Arithmetic Series

Example: Given the sum of the first 15 terms of an arithmetic sequence is 165 and the first term is , find… the common difference.

the 15th term.

the explicit formula for the sequence.

the sum of the first 20 terms of the sequence.

Arithmetic Series

Application of Arithmetic SeriesA corner section of a stadium has 14 seats along the front row and adds one more seat to each successive row. If the top row has 35 seats, how many seats are in that section?

Arithmetic Series

Homework

Arithmetic Sequences

Pre-precal review Set J Extra Practice

Textbook p. 605 #1-25 Odd

Sign up to receive texts from me (assignments, extra credit, etc.)

2nd period: Text the message honeycutt2 to 81010 3rd period: Text the message honeycutt3 to 81010