1
Lesson Plan #067
Date: Monday April 3rd, 2017
Class: Pre-calculus
Topic: Sequences
Aim: How can we determine if a sequence converges?
Objectives:
1) Students will be able to determine if a sequence converges
HW# 067:
1) Find the next 2 terms in each sequence
A) 3, -6, 12, -24, …
B) 1, 4, 10, 19, …
2) Find the first 4 terms of the sequence defined by an  (1) n 1  n
3) Find the 3rd term of the sequence an   an 1   5an 1  4 , where a1  3 and n  2
2
4) Determine whether each sequence is convergent or divergent:
A) an 
5n  6
6
B) an 
an 1  3
where a1  9 and n  2
2
5) Find S 8 in the sequence an  an1  (18  n) where a1  1 and n  2 .
Do Now:
1) A) Find the next 4 terms of the sequence 2, 5, 10, 17, …
B) Write a rule for the preceding sequence
2) Find the next 4 terms of the sequence defined by an  2n  1
n
Procedure:
Write the Aim and Do Now
Get students working!
Take attendance
Give back work
Go over the HW
Collect HW
Go over the Do Now
Assignment #1:
Find the first four terms of the sequence defined as an  n  10 .
3
Comment:
th
The above sequence was defined explicitly, in other words, the n term
recursively, that is the n
th
term
an as a function of n . Sequences can also be defined
an is defined as a function of the previous term an 1 .
Assignment #2:
Find the fifth term of the recursively defined sequence
an  an1  2n  1 , where a1  1 and n  2 .
2
Comment: Video on entering recursive functions in TI 84.
https://www.youtube.com/watch?v=kt1SQ2z3zV4
Comment:
If the terms of a sequence approach a unique number, then we can say that sequence converges to that number. If the
terms of a sequence do not approach a unique number, then the sequence diverges.
Assignment #3:
Determine if the sequence defined as an  3n  12 is convergent or divergent.
Assignment #4:
Determine whether each sequence defined below is convergent or divergent.
1
2
A) an   an 1 , where a1  36 and n  2 .
B) an
 1

n
4n  1
n
Comment: A series is the indicated sum of all the terms in a sequence. The sum of the first n terms of a series is
called the nth partial sum and is denoted S n .
Assignment #5:
First the fourth partial sum S 4 of an   2   3
n
Assignment #6:
Find S 3 of an 
4
10 n
Assignment #7:
Find the sixth partial sum of an  (0.5)  an1  , where a1  8 and n  2
Assignment #8:
7
Evaluate

3
6n  3
2
3
Assignment #9:
2n
Find a4 of an 
 n  1!
Assignment #10:
Express the sum using summation notation:
13  23  33  ...  73
Assignment #10:
Express the sum below using summation notation:
1 1 1
1
1  
 ...  n1
3 9 27
3
Assignment #11:
Simplify the factorial expression:
 2n  1!
(2n)!
Assignment #12:
A deposit of $6000 is made in an account that earns 6% interest compounded quarterly. The balance in the account
n
 0.06 
after n quarters is given by the sequence an  6000 1 
 . Find the balance in the account after 6 years.
4 

Assignment #13:
 1 x 2 n
Find a4 of an 
 2n  !
n
Assignment #14:
Find the first five terms of the sequence an 
1
1

, and then find an expression for the nth partial sum.
2n 2n  2