Honors Pre AP Calculus
Sections 9.1-9.3: Sequences and Series
1)
Name ___________________________
Date _________________
Determine whether each sequence is arithmetic, geometric or neither. Find the explicit formula for a n
for each sequence. a)
1 ,
1
4
,
1
9
,
1
16
1
,
25
,...
b) 12, 15, 18, 21, … c) 100, -50, 25, -12.5, … d)
1
2
,

1
4
,
1
8
,

1
16
,...
e) 3, 7, 11, 15, 19, … f)
1
2
,
1
2
,
3
4
,
3
2
,
15
4
...
2) Find x if the sequence
4 , x ,
3
2 x
is: a) arithmetic b) geometric

3) Simplify. a)
10 !

3 !
4 !

6 !
b)
( n
 n !
2 )!
4)
5)
6)
7)
Give the recursive formula for the sequence: 1, 2, 5, 26, 677, …
Give the explicit formula for the sequence: 1, 2, 6, 24, 120, 720, …
Find the 11 th term of the arithmetic sequence with a
1

15
and
Find the 9 th term of the geometric sequence with a
1

8
and a
2 d

4
.

8 5
.

8) Find 4 arithmetic means between -27 and 28.
9) Find 2 geometric means between 
1
5
and 
8
135
.
10) Find S
50
: 5 + 10 + 15 + 20 + …
11) Find the sum of all positive 3 digit numbers divisible by 6.
12) Find the sum of the series:
27

9

3

...

13) Express
48

24

12

6

...
using Sigma Notation.
14) Express 
27

9

3

1

1
3

1
9
...
using Sigma Notation.
15) Express
7

14

28

...

896
using Sigma Notation.
16) Find S for the geometric sequence: 
6 , 5 ,

25
6
,
125
36
, ...
. Leave answers in fraction form.
17) Evaluate: k
6 

1
32

1
4 k

1
Round to the nearest hundredth.

18) WEIGHTS Nathan has a collection of barbells for his home gym. He has 2 barbells for every
5 pounds starting at 5 pounds and going up to 80 pounds. What is the total weight of all his barbells?
19) TRIANGLES A triangle is made of congruent equilateral triangles as shown in the figure. a.
Starting from the top, each additional row of triangles has more and more triangles in it.
Write a formula for the number of triangles in row n. b.
If the large triangle consists of N rows of small triangles, how many small triangles are there in the large triangle? Write your answer using sigma notation.
c. Evaluate the sum you wrote for part b.

20) MOORE’S LAW Gordon Moore, co-founder of Intel, suggested that the number of transistors on a square inch of integrated circuit in a computer chip would double every 18 months. Assuming Moore’s law is true, how many times as many transistors would you expect on a square inch of integrated circuit every 18 months for the next 6 years?
21 ) TEACHING A teacher teaches 8 students how to fold an origami model. Each of these students goes on to teach 8 students of their own how to fold the same model. If this teaching process goes on for n generations, how many people will know how to fold the origami model?
22) EDUCATION Trevor Koba has opened an English Language School in Isehara, Japan. He began with 26 students. If he enrolls 3 new students each week, in how many weeks will he have 101 students?
23) SALARIES Yolanda interviewed for a job that promised her a starting salary of $32,000 with a $1250 raise at the end of each year. What will her salary be during her sixth year if she accepts the job?