Algebra 2/Trig 1
Sequence and Series #4 (Test Review)
Name
Block
Key
Date
Determine the pattern and write the equation for the given sequences.
1. 4, 7, 10, 13, 16, 19, 22, …
Add 3
2. 6, 12, 24, 48, 96, …
Multiply by 2
an  4  3(n  1)
an  6  2
n 1
100 100 100 100
,
,
,
3
9 27 81
1
Multiply by
3
3. 100,
1
an  100   
3
4. 1, 4, 9, 16, 25, 36, 49, 64, 81, …
Perfect Squares
n 1
an  n 2
Determine the pattern, write the rule (equation) for the given sequence then determine the
desired terms.
5. 6, 8, 10, 12, 14, 16, 18, 20, …
6. 5, 25, 125, 625, 3125, 15625, …
Find a15 and a34
Find a2 and a11
Add 2
Multiply by 5
n 1
an  6  2(n  1)
an  5  5
a15  6  2(15  1)
a2  25
or
a15  34
b/c it is given
a34  6  2(34  1)
a11  5  5
a34  72
a2  5  5
21
a2  25
111
a11  48828125
Determine the desired terms of the following sequences.
7. an  4  (n  1)  5
8. an  n (n  1)
1
9. an  384   
2
a1 = 4
a1 = 2
a1 = 384
a10 = 49
a2 = 6
a2 = 192
a256 = 1279
a3 = 12
a3 = 96
a20 = 420
a8 = 3
a56 = 3192
a13 =
3
32
n 1
Determine the pattern, then write the rule(equation) for the following series.
Write using sigma notation then determine the sum of the following series.
10. 4 + 20 + 100 + 500 + 2500 + 12500 + 62500
11. 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26 + 29
Multiply by 5
Add 3
an  5  3 n  1 
n 1
an  4  5
7
9
4 5
 5  3 n  1
Option 1: the sum can be found by
adding all the numbers
Sum = 78124
Option 1: the sum can be found by
adding all the numbers
Sum = 153
Option 2: use the Sn formula
 1  57 
S7  4 

 15 
S7  78124
Option 2: use the Sn formula
n 1
n 1
n 1
9
5  29 
2
S9  153
S9 
Write the following sequences in sigma notation then determine the sum of the following series.
12. an  92  (n  1)  3
Sum of the first 13 terms. 13.
13
9
 92  (n  1)  3
n 1
92, 89, 86, 83,  Subtract 3
13
 92  a13 
2
need to know a13 first
S13 
a13  92  (13  1)  3
a13  56
13
 92  56
2
S13  962
S13 
14. an  (n  1)  6
Sum of the first 42 terms.
42
n 1
0,6,12,18...
42
 0  a42 
2
need to know a42 first
S42 
a42   42  1   6
a42  246
42
 0  246
2
 5166
S42 
S42
n 1 
n 1
3,12,36,...
multiply by 4
 1  49 
S9  3 

 14 
S9  262143
15.
n 1
an  7  2
 7  2
add 6
Sum of the first 9 terms.
 3  4
7
 n  1  6
n 1
an  3  4
n 1 
n 1
7,14,28,56...
multiply by 2
 1  27 
S7  7 

1

2


S7  889
Sum of the first 7 terms.
Find the sum given the following sigma notation.
9
90
 4n
16.
17.
n 1
4, 8, 12, 16, … add 4
Option 1: Write it out and add
4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36
Sum = 180
Option 2: Use the Sn
9
S 9   4  a9 
2
a9  4  9 
 4n
n 1
4, 8, 12, 16, … add 4
S
90
 4  a90 
2
 4  90 
90
a90

a90  360
90
 4  360 
2
 16380
S90 
S90
a9  36
9
 4  36
2
S9  180
S9 
7
7
n 2
18.
19.
n 1
n 1
 3   6
n 1
3, 18, 108, 648, … multiply by 6
1, 4, 9, 16, … perfect squares
Option 1: Write it out and add
1 + 4 + 9 + 16 + 25 + 36 + 49
Sum = 140
Option 2: Use the perfect square formula
S

7
7  7  1 2  7  1 
S7  140
20.
6
128
 8  n  1  3
n 1
Option 1: Write it out and add
3 + 18 + 108 + 648 + 3888 + 23328 + 139968
Sum = 167961
Option 2: Use an Sn formula
 1  67 
S 7  3

 16 
S7  167961
20
21.
n
2
n 1
8, 11, 14, 17, … add 3
128
S128 
8  a128 
2
need to know a128 first
a128  8  128  1   3
a128  389
128
8  389 
2
 25408
S128 
S128
1, 4, 9, 16, … perfect squares
Use the perfect square formula
20 20  1 2  20  1 
S 20 
6
S20  2870
22. The first row of a concert hall has 25 seats and each row after the first has one more
seat than the row before it. There are 32 rows of seats. How many total seats are there?
25, 26, 27, 28, 29, …
Add 1
an  25  1 n  1 
32
25  a32 
2
32

25  56
2
 1296
need to know a32 first
S32 
S32
S32
a32  25  1 32  1 
a32  56
23. You have started a savings account and placed $1500 into the account with a 3% interest
rate. How much money would be in your account after 8 years?
(Note: Since the interest rate is 3% plus the present value, each year there will be 1.03 more)
n 1
an  1500  1.03
81
a8  1500  1.03
a8  1844.81
24. Rolls of toilet paper are on sale at the grocery store and are being displayed at the end
of the aisle. There are 16 rolls on the bottom row, 15 on the row above, 14 on the row above
that and so on, until there is only 1 roll in the top row. How many total rolls of toilet paper
are on display?
16, 15, 14, 13, … 1
or
Just add the numbers together
16
S16 
16  1 

16 + 15 + 14 + 13 + … + 3 + 2 + 1
2
S16  136
Sum = 136
25. A virus goes through a computer, infecting files. Five files were infected initially and
the total number of files infected doubles every minute.
a) How many total files will be infected in 20 minutes?
b) Algebraically determine at what minute 100,000 new files would be infected.
an  5  2 
n 1
100000  5  2 
n 1
an  5  2 
n 1
a)
S20
S20
 1  220 
 5

 12 
 5242875
20000  2n 1
100000  5  2 
n 1
b) 20000  2n 1
log2 20000  n  1
n  15.288minutes
log20000  log2n 1
or
log20000  (n  1)log2
log20000  n log2  log2
log20000  log2  n log2
log20000  log2
n
log2
n  15.288minutes