Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
SEQUENCES
Arit h m e t ic Se que nce s , Part 1
In an arithmetic sequence, the same amount is always added to
get from one term to the next.
The amount that is added to get to each next term is called the
common difference.
Arithmetic
sequences
are really just
skip-counting
patterns!
Fill in the blanks to complete the
arithmetic sequence below.
EXAMPLE
AAAAAAAAAAAAAAA
9GDGIKPD[ſPFKPIVJGEQOOQPFKHHGTGPEG6QIGVHTQOVQ
KPVJKUUGSWGPEGYGCFFVJGEQOOQPFKHHGTGPEGVKOGU
AAAAAAAAAAAAAAA
#FFKPIVJGEQOOQPFKHHGTGPEGVKOGUCFFUCVQVCNQH
Ŧ5QVJGEQOOQPFKHHGTGPEGKUÒ
9GWUGVJKUVQſPFVJGOKUUKPIVGTOUCUUJQYP
+12
+12
+12
+12
+12
+12
AAAAAAAAAAAAAAA
7
31 43 55
79
PRACTICE
35.
Find the common difference for each arithmetic sequence below.
36.
35. AAAAAAAA
36. AAAAAAAA
37.
38.
37. AAAAAAAA
AAAAAA
38. AAAAAAAA
39.
AAAAAA
40.
1
AAAAAAAA 2, ...
39. AAAAAAAA
40. AAAAAAAA
12
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Beast Academy Practice 5C
Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
SE QUE NC ES
Arithmetic Sequence s, P a rt 1
PRACTICE
Fill in the blanks to complete each arithmetic sequence below.
41.
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42.
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43.
AAAAAAAAAAAAAAAAAAAA 2 , AAAAA
44.
AAAAAAAAAAAAAAAAAAAAAAAAA
1
PRACTICE
Answer each question below.
45.
9JCVKUVJGEQOOQPFKHHGTGPEGQHCPCTKVJOGVKEUGSWGPEGYJQUGſTUV
term is 25 and whose tenth term is 115?
45. AAAAAAAA
46.
9JCVKUVJGEQOOQPFKHHGTGPEGQHCPCTKVJOGVKEUGSWGPEGYJQUGrd
1
1
term is and whose 25th term is 2 ?
46. AAAAAAAA
47.
An arithmetic sequence has 10thVGTOCPFth term 68. What is the
20th term of the sequence?
47. AAAAAAAA
48.
#PCTKVJOGVKEUGSWGPEGJCUſXGVGTOU6JGſTUVVGTOKUCPFVJG
UWOQHCNNſXGVGTOUKU9JCVKUVJGEQOOQPFKHHGTGPEG!
48. AAAAAAAA
Beast Academy Practice 5C
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13
Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
S
EQ
UEN
A ri
t h me
tic CES
Sequences ,
EXAMPLE
Part 1
What is the 50th term of the arithmetic sequence below?
6JGſTUVVGTOQHVJGCTKVJOGVKEUGSWGPEGKUCPFVJG
EQOOQPFKHHGTGPEGKU
To get to the 2nd term, we add 1 three to 2.
6QIGVVQVJGrd term, we add 2 threes to 2.
6QIGVVQVJGthVGTOYGCFFVJTGGUVQ
To get to the 50thVGTOYGCFFVJTGGUVQ
So, the 50thVGTOKU
149.
PRACTICE
Find the value of the missing term listed for
each arithmetic sequence below.
49.
51.
PRACTICE
10th
15th
50.
52.
th
100th
Answer each question below.
53.
9JCVKUVJGthVGTOQHCPCTKVJOGVKEUGSWGPEGYJQUGſTUVVGTOKU
and whose common difference is 8?
53. AAAAAAAA
54.
9JCVKUVJGſTUVVGTOQHCPCTKVJOGVKEUGSWGPEGYJQUGth term is
1
CPFYJQUGEQOOQPFKHHGTGPEGKU ?
54. AAAAAAAA
55.
The 12th and 15th terms of an arithmetic sequence are 85 and 106.
9JCVKUVJGſTUVVGTOQHVJGUGSWGPEG!
55. AAAAAAAA
14
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Beast Academy Practice 5C
Excerpt from Beast Academy 5C. (C) 2016 www.BeastAcademy.com
SE QUE NC ES
Arithmetic Sequence s, P a rt 1
EXAMPLE
Write an expression for the nth term of the arithmetic
sequence below.
You can check
your answer
by plugging in
values for n!
6JGſTUVVGTOQHVJGUGSWGPEGKUCPFVJGEQOOQPFKHHGTGPEGKU
For example,
we know the 3rd
+5 +5 +5 +5 +5
term is 9. So, we can
plug in n=3 to get
5(3)–6=9. 9
To get the 2ndVGTOYGCFFſXGVQ
6QIGVVJGrdVGTOYGCFFſXGUVQ
6QIGVVJGthVGTOYGCFFſXGUVQ
To get the nth term, we add (nŦſXGUVQ
So, the nthVGTOKU
nŦ&KUVTKDWVKPIVJGCPFUKORNKH[KPIIKXGU
nŦnŦ
5nŦ.
PRACTICE
9TKVGCUKORNKſGFGZRTGUUKQPHQTVJGnth term
of each arithmetic sequence below.
56.
58.
PRACTICE
n
th
nth
57.
59.
9 5 11
, , ,
2 ...,
nth
nth
Answer each question below. Simplify all expressions.
60.
#PCTKVJOGVKEUGSWGPEGJCUſTUVVGTOaCPFEQOOQPFKHHGTGPEG
Write an expression for the 20th term of the sequence.
60. AAAAAAAAAAAAA
61.
#PCTKVJOGVKEUGSWGPEGJCUſTUVVGTOCPFEQOOQPFKHHGTGPEGd.
Write an expression for the 101st term of the sequence.
61. AAAAAAAAAAAAA
62.
In an arithmetic sequence, the 1st term is 20, the 2ndVGTOKUCPF
the kth term is 500. What is k?
Beast Academy Practice 5C
62. kAAAAAAAA
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15