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To begin with, let’s revisit what a sequence is. A sequence is simply a series or grouping of things arranged in a specific order. In math, a sequence is merely a series of numbers arranged in a numeric order. For example, 10, 20, 40, 80, 160, 320… is a series of numbers that go in sequential order from lowest number to highest number.

There are two different types of number sequences found in math. For this quiz we will be dealing with geometric sequences. What is a geometric sequence? A geometric sequence is a series of numbers in which each preceding term or number is __multiplied__ by the same constant number. For example, let’s look at the following series.

**1, 2, 4, 8, 16, 32, 64, 128**

In this series, the constant number is “2” and each preceding number is multiplied by “2” as follows:

1 x 2 = 2

2 x 2 = 4

4 x 2 = 8

8 x 2 = 16

16 x 2 = 32

32 x 2 = 64

64 x 2 = 128

There is an easy hint that will help you find the missing constant number and that is by dividing the second number in the series by the first number. So looking at our series above you would have 2 ÷ 1 = 2. The number “2” was the constant number here.

1.

In the following geometric sequence, determine what the constant number is.

(4, 28, 196, 1,372, 9,604)

(4, 28, 196, 1,372, 9,604)

6

7

8

9

A quick way to find the constant number in this series is to divide the second number by the first number so 28 ÷ 4 = 7. Now let’s multiply 28 x 7 = 196. Yes, it appears that the common factor is the number “7”. Answer (b) is the correct answer

2.

Which series of numbers below is NOT a geometric sequence?

4, 16, 64, 256, 1,024, 4,096

17, 22, 27, 32, 37, 42, 47

16, 32, 64, 128, 256, 512

6, 36, 216, 1,296, 7,776

Answer (a) can be figured by multiplying each preceding number by the number “4” so it is a geometric sequence. Answer (c) can be figured by multiplying each preceding number by the number “2” so it is a geometric sequence. Answer (d) can be figured by multiplying the number “6” to each proceeding number and it is a geometric sequence. However, with Answer (b), it appears that the constant number “5” is being added making it an arithmetic sequence which is NOT a geometric sequence. Therefore, Answer (b) is the correct answer

3.

In the following geometric sequence, which number is missing from the series?

(11, 33, 99, 297, _____, 2,673, 8,019)

(11, 33, 99, 297, _____, 2,673, 8,019)

887

889

890

891

A quick way to find the constant number in this series is to divide the second number by the first number so 33 ÷ 11 = 3. Now let’s multiply 33 x 3 = 99. Yes, it appears that the common factor is the number “3” and it is being multiplied to the preceding number. So let’s now multiply 297 x 3 = 891. Answer (d) is the correct answer

4.

In the following geometric sequence, which number is missing from the series?

(2, 200, 20,000, 2,000,000, _____)

(2, 200, 20,000, 2,000,000, _____)

200,000,000

20,000,000

200,000

2,000

A quick way to find the constant number in this series is to divide the second number by the first number in the series so 200 ÷ 2 = 100. Now multiply 200 x 100 = 20,000. Yes, 100 appears to be the common factor so 2,000,000 x 100 = 200,000,000. Answer (a) is the correct answer

5.

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, -480, -9,600, -192,000, -3,840,000

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. Answers (a), (b) and (d) are neither an arithmetic sequence nor a geometric sequence. Answer (c) on the other hand is figured by multiplying the number “20” to each preceding number and continues throughout the series of numbers making it a geometric sequence. Answer (c) is the correct answer

6.

Which series of numbers below is NOT a geometric sequence?

8, 10, 12, 14, 16, 18, 20, 22

3, 9, 27, 81, 243, 729

5, 25, 125, 625, 3,125, 15,625

2, 4, 6, 12, 24, 48, 96

Answer (b) can be figured by multiplying each preceding number by the number “3” so it is a geometric sequence. Answer (c) can be figured by multiplying each preceding number by the number “5” so it, too, is a geometric sequence. Answer (d) can be figured by multiplying the number “2” to each proceeding number making it a geometric sequence. However, with Answer (a), it appears that the number “2” is being added to each preceding number. This makes this an arithmetic sequence and NOT a geometric sequence. Answer (a) is the correct answer

7.

In the following geometric sequence, determine what the constant number is.

(27, 54, 108, 216, 432, 864)

(27, 54, 108, 216, 432, 864)

2

4

6

8

A quick way to find the constant number in this series is to divide the second number by the first number so 54 ÷ 27 = 2. Now let’s multiply 54 x 2 = 108. Yes, it appears that the common factor is the number “2”. Answer (a) is the correct answer

8.

Which series of numbers below is a geometric sequence?

2, 6, 10, 14, 18, 22, 26

7, 15, 23, 31, 39, 47, 55

4, 4.8, 5.76, 6.912, 8.2944, 9.95328

1, 13, 25, 37, 49, 61, 73

Answer (a) is figured by adding the number “4” to each preceding number. Answer (b) is figured by adding the number “8” to each preceding number and Answer (d) is figured by adding the number “12” to each preceding number. Although these are each a sequence, they are arithmetic sequences and not geometric sequences. Answer (c) on the other hand is figured by multiplying the number “1.2” to each preceding number and continues throughout the series of numbers making it a geometric sequence. Answer (c) is the correct answer

9.

In the following geometric sequence, which number is missing from the series?

(3, 21, 147, 1,029, _____, 50,421)

(3, 21, 147, 1,029, _____, 50,421)

6,174

7,203

5,145

8,232

A quick way to find the constant number in this series is to divide the second number by the first number so 21 ÷ 3 = 7. Now let’s multiply 21 x 7 = 147. Yes, it appears that the common factor is the number “7” and it is being multiplied to the preceding number. So let’s now multiply 1,029 x 7 = 7,203. This tells us that Answer (b) is the correct answer

10.

Which series of numbers below is a geometric sequence?

4, 20, 36, 52, 68, 84, 100

5, 12, 19, 26, 33, 40, 48, 55

4.5, 14.5, 24.5, 34.5, 44.5, 55.5

1, 3.5, 12.25, 42.875, 150.0625, 525.21875

Answer (a) is figured by adding the constant number “16” which makes it an arithmetic sequence. Answer (b) is figured by adding the number “7” but then it breaks at the number 40 and it is neither an arithmetic sequence nor a geometric sequence. Answer (c) is figured by adding the number “10” and is an arithmetic sequence, not a geometric sequence. Answer (d) on the other hand is figured by multiplying the number “3.5” to each preceding number and continues throughout the series of numbers making it a geometric sequence. Answer (d) is the correct answer