Precalculus
Theorem
Unit 9 – Sequences, Series, & Binomial
Name
Date
Tuesday May 20, 2014
Classwork/Homework: Review #1 2014
Example 1a Use the Binomial Theorem to find the first three term of
 2m  7 
Now you try 1b Use the Binomial Theorem to find the first three term of
Example 2a Find the 9th term in the expansion of  g  2k  .
14
Now you try 2b Find the 6th term in the expansion of  7w  z  .
8
Example 3a Find the coefficient of the c 4 d 2 term of  9c  2d  .
6
Now you try 3b Find the coefficient of the p 2 q5 term of  3 p  2q  .
7
6
.
 x  3y 
5
.
Example 4a An assembly line that produces light bulbs is not operating well. In the past approximately 1% of all the
light bulbs from this assembly line have been defective. Assuming that the defective light bulbs are randomly
distributed, what is the probability that a 12-bulb carton of light bulbs produced by this assembly line will contain
exactly three defective light bulbs?
Now you try 4b…A soccer goalie blocks shots with 70% accuracy. What is the probability that the goalie will block
exactly 8 of the 10 shots teammates attempt at the end of practice?
Example 5a An assembly line that produces light bulbs is not operating well. In the past approximately 1% of all the
light bulbs from this assembly line have been defective. Assuming that the defective light bulbs are randomly
distributed, what is the probability that a 12-bulb carton of light bulbs produced by this assembly line will contain
more than one defective light bulb?
Now you try 5b…A soccer goalie blocks shots with 70% accuracy. What is the probability that the goalie will block
at least 9 of the 10 shots teammates attempt at the end of practice?
Example 6a A person just fitted for contact lenses is told to wear them only 2 hours the first day and to increase the
length of time by 20 minutes each day. After how many days will the person be able to wear the contacts for 14 hours
Now you try 6b… The cost of a new ATV (all-terrain vehicle) is $7200. It depreciates at 18% per year. Write an nth
term sequence that gives the value of the ATV in terms of time. Find the value of the ATV when it is seven years old.
Example 7a You have an ear infection and are told to take a 250 mg tablet of ampicillin four times a day (every six
hours). It is known that at the end of six hours, about 4% of the drug is still in the body. What quantity of the drug is
in the body right after the fortieth dose?
Now you try 7b…A snail is crawling straight up a wall. The first hour it climbs 16 inches and each succeeding hour,
it climbs only three-fourths the distance it climbed the previous hour. Assume the pattern continues. What is the total
distance the snail has climbed in seven hours?
Example
8a: Find the nth term of the sequence.
–5, 0, 5, 10, 15, 20,….
9a: Find the nth term of the sequence.
100, 50, 25, 12.5, …
10a: Find the nth term of the sequence.
2 3 4 5
, , , ,...
5 8 11 14
Now you try…
8b: Find the nth term of the sequence.
28, 20, 12, 4, -4, -12,….
9b: Find the nth term of the sequence.
1, -3, 9, -27, 81,…
10b: Find the nth term of the sequence.
1 8 27 81
, , , ,...
2 3 4 5
Example
11a: Find the nth term of the sequence.
a1  15 , d  2
Now you try…
11b: Find the nth term of the sequence.
2
a1  2 , r 
3
12a: Find the nth term of the arithmetic sequence.
12b: Find the nth term of the arithmetic sequence.
a2  18 , a8  6
a5  20 , a12  1
13a: Find the nth term of the geometric sequence.
2
a2  18 , a5 
3
13b: Find the nth term of the geometric sequence.
4
a3  4 , a7 
81
14a: Find the sum of the first 18 terms of the sequence.
14b: Find the sum of the first 80 terms of the following
sequence. 11 + 17 + 23 + …
–8, –1, 6, 13, 20, 27,….
3 3
,
, ….
2 4
Find the sum of the first n terms of the sequence. n=11
.
15a: Consider the sequence: 6, –3,
15b: Consider the sequence: 14, 8, 2, –4 ,….
Find the sum of the first n terms of the sequence.
n=9
16a: Find the sum of the series below.
2 + 5 + 8 + 11 + …+ 53
16b: Find the sum of the sequence below.
3, 6, 12, 24, … , 12288
17a: Find the sum of the first 15 terms of the series.
5,-15, 45, – 135,….
17b: Find the sum of the first 10 terms of the following
sequence. 3 + 9 + 27 + 81 + …
18a: If possible, find the sum of the series.
9 27 81
3 
  ...
4 16 64
18b: If possible, find the sum of the series.
6 36 216
1  
 ...
5 25 125
50
19a: Evaluate.
1
2n6
n 1
 1
2  

4
n 1 
22
19b: Evaluate
n 1
28
20a: Evaluate.
1
2n6
n 6
35
20b: Evaluate
2
 2n  3
n 5