Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Sequence and Series Syllabus and Hw, Lecture notes of Geometry

Unit 14: Sequences and Series ... Worksheet A: Introduction to Sequences ... Find the first 4 terms of the sequence given the explicit formula.

Typology: Lecture notes

2021/2022

Uploaded on 08/01/2022

hal_s95
hal_s95 🇵🇭

4.4

(652)

10K documents

1 / 13

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Geometry and Finite Math X
Unit 14: Sequences and Series
Day Lesson Homework if
completed
Day 1 Numeric Sequences Worksheet
A
Day 2 Explicit Formulas Worksheet
B
Day 3 Arithmetic and
Geometric Sequences
Worksheet C
Day 4 Pascal’s Triangle and
Fibonacci Sequence
Quiz Review
Worksheet
D
Day 5 Quiz
Begin Recursion
Worksheet E
Day 6 Recursion Worksheet F
Day 7 Sums/Sigma Notation
Worksheet
G
Day 8 Review Worksheet
H
Day 9 Test
pf3
pf4
pf5
pf8
pf9
pfa
pfd

Partial preview of the text

Download Sequence and Series Syllabus and Hw and more Lecture notes Geometry in PDF only on Docsity!

Geometry and Finite Math X

Unit 14: Sequences and Series

Day Lesson Homework

if

completed

Day 1 Numeric Sequences Worksheet

A

Day 2 Explicit Formulas Worksheet

B

Day 3 Arithmetic and

Geometric Sequences

Worksheet C

Day 4 Pascal’s Triangle and

Fibonacci Sequence

Quiz Review

Worksheet

D

Day 5 Quiz

Begin Recursion

Worksheet E

Day 6 Recursion Worksheet F

Day 7 Sums/Sigma Notation Worksheet

G

Day 8 Review Worksheet

H

Day 9 Test

Worksheet A: Introduction to Sequences

For each sequence, find the next 4 terms. Describe the pattern in words.

The following are multiple choice questions. Find the next three terms of each sequence. Next to the problem, describe the pattern in words. Describe the Pattern:

Worksheet B: nth term of a sequence

Multiple Choice: Circle the correct answer.

Find the first 4 terms of the sequence given the explicit formula.

6. Use the explicit formulas below to find a 1 , a 2 and a 10 for each formula. Show your work.

a. an = n

3

+ 4 b. an = -5n + 3

c. an = d. an = 2n^ (this is 2 raised to the

n-power, not 2 times n.)

7. Consider the following sequences. Write the explicit formula for each.

a. 5, 6, 7, 8, 9, …… an = _______________________

b. 4, 8, 12, 16, 20…… an = _______________________

a. 4, 16, 64, 256, 1024…… an = _______________________

6. Find the first 4 terms of each sequence. Determine whether each is arithmetic, geometric

or neither. If so, find the common difference or common ratio.

a. b.

c. d.

7. Karla opens a savings account at her bank with $500, compounded monthly with an

annual rate of 2.5%

a. How much is her monthly rate of interest?

b. How much will she have in her account after 1 month?

c. How much after 2 months?

3 months?

d. How much is in her account after 1-year?

e. Is compound interest an arithmetic or a geometric sequence?

Homework Worksheet D

  1. Fill in the blanks to Pascal’s Triangle (There are blanks throughout the triangle!)
  2. Find the sum of numbers in row 2 (see row labels) ___________
  3. Find the sum of the numbers in row 3 _____________
  4. Find the sum of the numbers in row 4 _____________
  5. Use the pattern from the previous 3 answers to find the sum of row 5 _____________ Check your answer by adding the numbers in row 5.
  6. Is the sum of numbers in the rows of Pascal’s triangle an arithmetic or geometric sequence? Explain your answer.
  7. Generate the next 6 terms of the Fibonacci Sequence.
  1. Bonus: Find one application of the Fibonacci Sequence in nature. Print your finding and bring it to class. Make sure you can understand your example!

Worksheet E: Recursion: HW after Quiz

Worksheet F: Recursively Defined Sequences

Write the recursive rule in WORDS. Then, find the first 5 terms (the first one is already given, so you really only have to find the next 4. Write the first one anyway!)

1

1

2

n^4 n

a

a (^) + a

=

=

1

1

n^2 n

a

a + a

1

1

8

1

2

n n

a

a (^) + a

=

=

1

1

3

n n^9

a

a (^) + a

=

= −

1

1

10

n^2 n^4

a

a (^) + a

=

= +

1

1

18

2 18 3

n n

a

a (^) + a

=

= +

Write the summation notation for the following:

  1. Explain the significance of the ( 1) − n +^1 in the expression

4 1 1

( 1) n (4 3) n

  • n =

∑ −^ +.

_________________________________________________________________________________

________________________________________________________________________________

_________________________________________________________________________________

15. Express the series 3 - 5 + 7 - 9 using sigma notation.