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Number Sequences - Mixing Arithmetic and Geometric Sequences
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By now you should understand that a sequence is a series or grouping of things arranged in a specific order and in math, it refers to a series of arranged numbers. There are two sequences – the arithmetic sequence and the geometric sequence.
1 .
In the following arithmetic sequence, which number is missing from the series?
(78, 83, 88, 93, _____, 103, 108)
(78, 83, 88, 93, _____, 103, 108)
96
97
98
99
A quick way to find the constant number in this series is to subtract the first number from the second number so 83 - 78 = 5. Now let’s see what happens if we add 5 to 83. 83 + 5 = 88. Yes, it appears that the common factor is the number “5”. So let’s now add 5 to 93. 93 + 5 = 98. Answer (c) is the correct answer
2 .
Which series of numbers below is a geometric sequence?
3, 21, 147, 1,028, 6,174
8, 16, 24, 32, 40, 48, 54
2, 22, 242, 2,662, 29,282
12, 24, 48, 68, 74, 98, 104
Answer (a) is figured by multiplying the number “7” but then it breaks at the number 147 so it is not a true sequence. Answer (b) is figured by adding the number “8” making it an arithmetic sequence. Answer (d) does not contain a constant number and is, therefore, not a true sequence. Answer (c) on the other hand is figured by multiplying the number “11” to each preceding number and continues throughout the series of numbers making it a geometric sequence. Answer (c) is the correct answer
3 .
In the following geometric sequence, determine what the constant number is.
(15, 45, 135, 405, 1,215)
(15, 45, 135, 405, 1,215)
3
4
5
6
A quick way to find the constant number in this series is to divide the second number by the first number so 45 ÷ 15 = 3. Now let’s multiply 45 x 3 = 135. Yes, it appears that the common factor is the number “3” and it is being multiplied to the preceding number. Answer (a) is the correct answer
4 .
Which series of numbers below is NOT a geometric sequence?
13, 26, 39, 52, 65, 78, 91
13, 26, 52, 104, 208, 416
13, 39, 117, 351, 1,053, 3,159
13, 52, 208, 832, 3,328, 13,312
Answer (b) can be figured by multiplying each preceding number by the constant number “2” so it is a geometric sequence. Answer (c) can be figured by multiplying by the constant number “3” so it is a geometric sequence. Answer (d) can be figured by multiplying each preceding number by the constant number 4 also making it a geometric sequence. However, Answer (a) can be figured by adding the constant number 13 to each preceding number making it an arithmetic sequence and NOT a geometric sequence. Answer (a) is the correct answer
5 .
Which series of numbers below is NOT a geometric sequence?
17, 289, 4,913, 83,521, 1,419,857
20, 30, 40, 50, 60, 70
13, 26, 52, 104, 208, 416
7, 28, 112, 448, 1,792, 7,168
Answer (a) can be figured by dividing the second number by the first number so 289 ÷ 17 = 17 and the constant number is used throughout the series so this is a geometric sequence. Answer (c) can be figured by multiplying by the constant number “2” making this a geometric sequence. Answer (d) can be figured by multiplying by the constant number “4” to each proceeding number making this a geometric sequence. However, with Answer (b), it appears that the constant number “10” is being added to each preceding number making this an arithmetic sequence and NOT a geometric sequence. Answer (b) is the correct answer
6 .
Which series of numbers below is a geometric sequence?
10, 20, 30, 35, 45, 50, 60
14, 15, 16, 17, 18, 19, 21, 22, 24, 25, 26
-24, -16, -8, 0, 8, 16, 24
48, 41, 34, 27, 21, 14, 7, 1
Answer (a) is figured by adding the number “10” but then it breaks at the number 30. Answer (b) is figured by adding the number “1” but then it breaks at the number 19. Answer (d) is figured by subtracting the number “7” but then it breaks at the number 27. Because of the break in adding or subtracting 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 “8” to each preceding number and continues throughout the series of numbers making it a geometric sequence. Answer (c) is the correct answer
7 .
In the following geometric sequence, which number is missing from the series?
(2, 18, 162, 1,458, _____, 118,098)
(2, 18, 162, 1,458, _____, 118,098)
13,022
13,102
13,112
13,122
A quick way to find the constant number in this series is to divide the second number by the first number so 18 ÷ 2 = 9. Now let’s multiply 18 x 9 = 162. Yes, it appears that the common factor is the number “9”. So multiply 1,458 x 9 = 13,122. This tells us that Answer (d) is the correct answer
8 .
In the following arithmetic sequence, determine what the constant number is.
(22, 40, 58, 76, 94, 112)
(22, 40, 58, 76, 94, 112)
16
18
14
12
A quick way to find the constant number in this series is to subtract the first number from the second number so 40 - 22 = 18. Now add 18 to 40 so 40 + 18 = 58. Yes, it appears that the common factor is the number “18”. Answer (b) is the correct answer
9 .
Which series of numbers below is NOT an arithmetic sequence?
10, 60, 360, 2,160, 12,960, 77,760
5, 10, 15, 20, 25, 30, 35, 40
12, 20, 28, 36, 44, 52, 60, 68
1, 51, 101, 151, 201, 251, 301
Answer (b) is figured by adding the constant number “5” to each preceding number making this an arithmetic sequence. Answer (c) is figured by adding the constant number “8” to the preceding number making this an arithmetic sequence. Answer (d) is figured by adding the constant number “50” to each preceding number making this an arithmetic sequence. Answer (a) on the other hand is figured by multiplying by the number “6” to each preceding number and continues throughout the series of numbers making it a geometric sequence. Answer (a) is the correct answer
10 .
In the following arithmetic sequence, which number is missing from the series?
(64, 52, 40, 28, __, 4)
(64, 52, 40, 28, __, 4)
14
16
17
18
A quick way to find the constant number in this series is to subtract the first number from the second number so 64 - 52 = 12. Now let’s see what happens if we subtract 12 from 52 so 52 - 12 = 40. Yes, it appears that the common factor is the number “12” and it is being subtracted from the preceding number. So let’s now subtract 12 from 28. 28 - 12 = 16. Answer (b) is the correct answer
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