442 Sequences and Series
Name:
1.
Date:
Evaluate:
3
X
(2t
7.
1)
Which expression represents the sum of the
sequence 3, 5, 7, 9, 11?
t=1
A.
5
X
(2n + 1)
B.
n=0
2.
Find the value of
4
X
C.
3(x + 1).
3.
Evaluate:
P3
4.
Evaluate:
P2
5.
Jonathan's teacher required him to express the
sum 23 , 43 , 45 , 56 , 67 using sigma notation. Jonathan
proposed four possible answers. Which of these
four answers is not correct?
6.
A.
P7
C.
P5
k=1
1
k
k
k+1
k+2
B.
P5
k
k+1
D.
P6
k
k+1
k=1
k=2
5
X
(2n + 1)
n=1
A.
P3 p
n=1 n
B.
P3
C.
P3
D.
P3
Express the sum 7 + 14 + 21 + 28 + : : : + 105
using sigma notation.
9.
Look at the sequence.
A.
n
n=0 n
n=1 n
8.
What is the next number in the sequence?
p3
The expression 1 + 2 + 3 is equivalent to
n
D.
15, 3, 0.6, 0.12, : : :
p
n=1 n
(3n + 1)
+ 1)
( 1)k 1
k=1
(2k 1)!
k=3
3n
n=1
n=1
x=2
k=0 (3 cos k
5
X
5
X
1
n
page 1
0.015
B.
0.024
C.
0.15
D. 0.24
442 Sequences and Series
10.
Tom formed a sequence of numbers using the
equation 2x + 1 =
as shown below.
12.
Sandra wrote the sequence below.
2, 5, 10, 17, : : :
Which equation represents the rule for nding the
nth term of this sequence?
an = 2n2
A.
an = n + 1
B.
C.
an = n2 + 1
D. an = 2n + 1
What are the rst 5 terms in Tom's sequence?
A.
3, 7, 15, 31, 62
B.
C.
3, 7, 15, 30, 61
D. 3, 7, 15, 30, 60
13.
3, 7, 15, 31, 63
Look at the recursive formula.
A1 = 6
For n > 1; An = A(n
1)
+4
What are the rst 4 terms of this sequence?
11.
A.
5, 6, 7, 8
B.
6, 10, 14, 18
C.
9, 12, 15, 18
D. 10, 14, 18, 22
Look at the gures below.
14.
How Many Stickers?
Maya made the designs shown below using
\Happy Face" stickers.
If the number of square units in the pattern of
gures continues to increase arithmetically as
shown, how many square units will be in the 9th
gure?
39 + 1
A.
9
B.
C.
9(3 + 1)
D. 1 + (3 9)
How many stickers would she need to make a
design with 25 rows in the same pattern? Show
the mathematics you use to get your answer and
explain your reasoning.
page 2
442 Sequences and Series
15.
An auditorium has 30 rows of seats. The rst row
has 40 seats. The second row has 42 seats. The
third row has 44 seats. Each successive row has
two more seats than the row before it. How many
seats are there in the 30th row?
18.
What is the area of the 13th
A.
70 seats
B.
74 seats
C.
98 seats
D. 100 seats
19.
16.
Four terms of a geometric sequence are shown
below.
4,
5
? , 100, 500, 2500, : : :
B.
10
C.
20
A.
6,144
B.
C.
24,576
D. 49,152
12,288
Look at this sequence.
A.
62
B.
34
C.
27
D.
13
D. 50
20.
17.
gure in this pattern?
What is the ninth term in the sequence?
What is the missing term in the sequence?
A.
Look at this pattern.
The rst ve terms of a linear sequence are shown
below.
Bricks are stacked in 25 layers. Except for the top
layer, which has three bricks, each layer has two
more bricks than the layer above it. How many
bricks are there altogether?
A.
624
B.
675
E.
none of the above
C.
325
D. 700
8, 6, 4, 2, 0,: : :
What is the 100th term in the sequence?
A.
192
B.
190
C.
108
D.
21.
90
page 3
The sum of the rst 100 positive integers is:
A.
5,050
B.
10,100
E.
none of the above
C.
7,500
D. 6,250
442 Sequences and Series
22.
The seventh term of the geometric sequence 9,
18, 36, : : : is:
A.
72
B.
54
E.
none of the above
C.
576
D.
26.
288
A.
27.
23.
The sum of the rst 5 terms in a geometric
progression, if the ratio is 31 and the rst term
is 2, is:
A.
242
81
B.
C.
163
81
D.
E.
none of the above
The sum of the rst fty positive odd integers
subtracted from the sum of the rst fty positive
even integers is:
28.
244
81
25.
Find the tenth term of the arithmetic sequence
with rst term 87 and common di erence of 5.
A.
42
B.
132
E.
none of the above
C.
13
29.
D. 15
30.
If the third term of an arithmetic series is 7 and
the twenty-third term is 43, what is the eleventh
term?
A.
E.
12
B.
27.5
C.
15.5
9
5
3
B.
11
C.
13
B.
4
3
C.
3
2
11
6
B.
11 6
D.
1
6!
E.
11
6!
D. 50
D. 15
D.
The nth term of the sequence 1,
E.
page 4
40
A.
C.
none of the above
C.
E.
100
E.
17
1
2
E.
1
3
The 6th term of the recursively de ned sequence
a(n 1)
with a1 = 11 and an =
is:
n
2 n
3
A.
D. 13
30
By adding the same constant to each of 20, 50,
and 100 a geometric progression results. The
common ratio is:
A.
24.
B.
If the fourth term of an arithmetic sequence is 5
and the ninth term is 20, the sixth term is:
A.
40
3
25
1
1+
2 n
3
2
3
2 n+1
3
C.
2 4
3, 9,
B.
4 n 1
3
D.
2 n 1
3
11 (6!)
: : : is:
442 Sequences and Series
31.
Find the next term in the sequence.
35.
625, 125, 25, 5, 1,
A.
5
B.
1
5
C.
5
1
5
D.
E.
25
Find the sum of the rst 20 terms of the geometric
series 2 6 + 18 54 + 2.
A.
3;486;784;400
B.
C.
1;162;261;466
D. 1,162,261,466
E.
32.
Given that 1 + 4 + 9 + 2 + 100 = 385,
6 + 21 + 46 + 81 + 2 + 501.
A.
1925
B.
1926
D. 1990
E.
2025
C.
1935
36.
The third term of a geometric sequence is 12 and
the fth term is 75. Determine the nth term of
the sequence if all of its terms are positive.
34.
26
B.
44
C.
54
D. 62
E.
E.
397
D. 19,900
B.
401
E.
94,109,400
C.
5
2
51 +
n
.
B.
63
(n
2
1).
D.
48
25
5
2
51 +
n 1
.
63
n.
2
12 + 63n.
68
37.
Let a1 = 1 and an = an 1 + 4 for n = 2; 3; 4; : : : .
Evaluate the sum a1 + a2 + a3 + 2 + a100 .
A.
48
25
C.
Find the fourth term of the in nite sequence
de ned recursively by a1 = 8 and ak+1 = 6k + ak .
A.
1,743,392,200
nd
A.
33.
1;743;392;200
What is the rst digit of the 30th term in the
sequence f5; 15; 45; 135; 405; : : :g?
A.
5050
page 5
1
B.
2
C.
3
D. 4
E.
5
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442 Sequences and Series
03/12/2013
1.
Answer:
9
21.
Answer:
A
2.
Answer:
36
22.
Answer:
C
3.
Answer:
4
23.
Answer:
A
4.
Answer:
5
6
24.
Answer:
A
5.
Answer:
B
25.
Answer:
D
6.
Answer:
D
26.
Answer:
A
7.
Answer:
D
27.
Answer:
B
28.
Answer:
A
29.
Answer:
E
30.
Answer:
D
31.
Answer:
B
32.
Answer:
C
33.
Answer:
B
34.
Answer:
D
8.
Answer:
P15
n=1 7n
9.
Answer:
B
10.
Answer:
B
11.
Answer:
D
12.
Answer:
C
13.
Answer:
B
14.
15.
Answer:
C
16.
Answer:
35.
Answer:
B
C
17.
Answer:
36.
Answer:
B
B
37.
Answer:
C
18.
19.
Answer:
B
20.
Answer:
B