Number Sequences - Arithmetic Sequences

Do you recognize number sequences?

Number Sequences - Arithmetic Sequences

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What is a sequence? Well, a sequence is a series of items such as a series of seats in a theater or a TV series. However, in math, a sequence refers to a series of numbers. For example, 1, 2, 3, 4, 5, 6… is a series of numbers that go in sequential order from lowest number to highest number.

The series, 59, 58, 57, 56, 55, 54… is a series of numbers that go in sequential order from highest number to lowest number.

In math there are two different types of number sequences and for this quiz we will be dealing with the arithmetic sequence. What is an arithmetic sequence?

Arithmetic sequence is a series of numbers in which each preceding term or number is added to or subtracted from the preceding number by the same constant number.

Let’s look at the following arithmetic sequence.

4, 8, 12, 16, 20, 24, 28, 32

In this series, the constant number is “4” and each preceding number has the number “4” added to it as follows:

4 + 4 = 8
8 + 4 = 12
12 + 4 = 16
16 + 4 = 20
20 + 4 = 24
24 + 4 = 28
28 + 4 = 32

Here is another arithmetic sequence.

57, 50, 43, 36, 29, 22, 15

In this series, the constant number is “7” and each preceding number has the number “7” subtracted from it as follows:

57 - 7 = 50
50 - 7 = 43
43 - 7 = 36
36 - 7 = 29
29 - 7 = 22
22 - 7 = 15

1.
In the following arithmetic sequence, which number is missing from the series?
(81, 75, 69, 63, _____, 51, 45)
58
57
56
55
A quick way to find the constant number in this series is to subtract the second number by the first number so 81 - 75 = 6. Now let’s see what happens if we subtract 6 from 69. 69 - 6 = 63. Yes, it appears that the common factor is the number “6” and it is being subtracted from the preceding number. So let’s now subtract 6 from 63. 63 - 6 = 57. Answer (b) is the correct answer
2.
Which series of numbers below is NOT an arithmetic sequence?
1, 11, 121, 1,331, 14.641, 161,051
-100, -75, -50, -25, 0, 25, 50, 75, 100
10,000, 7,000, 4,000, 1,000, -2,000, -5,000
1, 13, 25, 37, 49, 61, 73
Answer (b) is figured by adding the constant number 25 to each preceding number and continues throughout the series so it is an arithmetic sequence. Answer (c) can be figured by subtracting the number “3,000” from each preceding number so it, too, is an arithmetic sequence. Answer (d) can be figured by adding the number “12” to each proceeding number so it, too is an arithmetic sequence. However, with Answer (a), it appears that each number is being multiplied by the constant number “11” making it a geometric sequence. Answer (a) is the correct answer
3.
In the following arithmetic sequence, which number is missing from the series?
(2, 104, 206, 308, _____, 512, 614)
402
410
412
414
A quick way to find the constant number in this series is to subtract the first number from the second number so 104 - 2 = 102. Now let’s see what happens if we add 102 to 104. 104 + 102 = 206. Yes, it appears that the common factor is the number “102”. So let’s now add 102 to 308. 308 + 102 = 410. Answer (b) is the correct answer
4.
Which series of numbers below is an arithmetic sequence?
1, 6, 11, 16, 22, 26, 31
9, 18, 27, 36, 44, 50, 59
5, 10, 15, 20, 25, 30, 35
8, 16, 24, 32, 39, 47, 56
Answer (a) is figured by adding the number “5” but then it breaks at the number 22. Answer (b) is figured by adding the number “9” but then it breaks at the number 36. Answer (d) is figured by adding the number “8” but then it breaks at the number 32. Because of the break in adding each preceding number by a constant number the series ends causing none of these answers to be correct. Answer (c) on the other hand is figured by adding the number “5” to each preceding number and continues throughout the series of numbers making it an arithmetic sequence. Answer (c) is the correct answer
5.
In the following arithmetic sequence, determine what the constant number is.
(67, 54, 41, 28, 15, 2)
9
12
13
14
A quick way to find the constant number in this series is to subtract the second number by the first number so 67 - 54 = 13. Now let’s see what happens if we subtract 13 from 54. 54 - 13 = 41. Yes, it appears that the common factor is the number “13”. Answer (c) is the correct answer
6.
Which series of numbers below is NOT an arithmetic sequence?
3, 6, 9, 12, 15, 18, 21
2, 6, 10, 14, 18, 22, 26
1, 4, 6, 11, 14, 16, 19
6, 8, 10, 12, 14, 16, 18
Answer (a) can be figured by adding “3” to each preceding number in the series making it an arithmetic sequence. Answer (b) can be figured by adding the number “4” to each preceding number and Answer (d) can be figured by adding the number “2” making both Answers (b) and (d) arithmetic sequences. Answer (c), however, does not have a repeated pattern or a constant number that is being used in the series. We can see the number “3” was used with “1” and “4” but the number “5” was used with the number “6”. This breaks the flow of the sequence so Answer (c) is NOT an arithmetic sequence. Therefore, Answer (c) is the correct answer
7.
Which series of numbers below is an arithmetic sequence?
10, 100, 1,000, 10,000, 100,000
1, 4, 8, 13, 19, 26, 34, 43
-24, -16, -8, -1, 7, 15, 24
58, 49, 40, 31, 22, 13, 4
Answer (a) is figured by multiplying by the number “10” which makes this a geometric sequence. Answer (b) does not have a constant number. Rather, it has a progressive number so it is not an arithmetic sequence. Answer (c) is figured by adding the number “8” but then it breaks at the number -8. Because of the break in adding to each preceding number it is not a true sequence. Answer (d) on the other hand is figured by subtracting the number “9” from each preceding number and continues throughout the series of numbers making it an arithmetic sequence. Answer (d) is the correct answer
8.
In the following arithmetic sequence, which number is missing from the series?
(9, 23, 37, 51, _____, 79, 93)
60
61
63
65
A quick way to find the constant number in this series is to subtract the first number from the second number so 23 - 9 = 14. Now let’s add 14 to 23 so 23 + 14 = 37. Yes, it appears that the common factor is the number “14”. Now if we add 14 to 51 we get 65. This tells us that Answer (d) is the correct answer
9.
Which series of numbers below is an arithmetic sequence?
3, 18, 108, 648, 3,888, 23,328
5, 18, 31, 44, 57, 70, 83, 96
4.5, 14.5, 24.5, 34.5, 44, 44.5, 50, 55.5
1, 7, 13, 19, 25, 32, 39, 46
Answer (a) is figured by multiplying the number “6”. As the constant is being multiplied it is a geometric sequence and not an arithmetic sequence. Answer (c) is figured by adding the number “10” but then it breaks at the number 34.5. Because of the break in adding the constant number it is not an arithmetic sequence. Answer (d) is figured by adding the number “6” but then it breaks at the number 25 so it is not a true arithmetic sequence. On the other hand, Answer (b) can be figured by adding the number 13 and it continues throughout making it an arithmetic sequence. Answer (b) is the correct answer
10.
In the following arithmetic sequence, determine what the constant number is.
(7, 28, 49, 70, 91, 112)
21
19
17
13
A quick way to find the constant number in this series is to subtract the first number in the series from the second number so 28 - 7 = 21. Now let’s add 21 to 28. 28 + 21 = 49. Now let’s add 21 to 70. 70 + 21 = 91. Yes, it appears that the common factor is the number “21”. Answer (a) is the correct answer
Author:  Christine G. Broome

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