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Ivan
3 years ago
9

Which of the following is not a geometric sequence?

Mathematics
2 answers:
makkiz [27]3 years ago
5 0

The sequence -7 , -5.8 , -4.6 , -3.4 , -2.2 is not a geometric sequence

Step-by-step explanation:

In the geometric sequence, there is a constant ratio between each two consecutive terms

To prove that a sequence is geometric

  • Find the ratio between each two consecutive terms \frac{a_{2}}{a_{1}} , \frac{a_{3}}{a_{2}} , \frac{a_{4}}{a_{3}} , .....
  • If all the answers give the same ratio, then the sequence is geometric, if not then the sequence is not geometric

The first sequence is 2.8 , 6.72 , 16.128 , 38.7072

∵ a_{1} = 2.8

∵ a_{2} = 6.72

∴ r=\frac{6.72}{2.8}=2.4

∵ a_{2} = 6.72

∵ a_{3} = 16.128

∴ r=\frac{16.128}{6.72}=2.4

∵ a_{3} = 16.128

∵ a_{4} = 38.7072

∴ r=\frac{38.7072}{16.128}=2.4

∵ All the ratios above are equal 2.4

∴ The sequence is a geometric sequence

The second sequence is -7, -5.8 , -4.6 , -3.4 , -2.2

∵ a_{1} = -7

∵ a_{2} = -5.8

∴ r=\frac{-5.8}{-7}=\frac{29}{35}

∵ a_{2} = -5.8

∵ a_{3} = -4.6

∴ r=\frac{-4.6}{-5.8}=\frac{23}{29}

∵ The first two ratios are not equal

∴ The sequence is not a geometric sequence

The third sequence is 1 , -3 , 9 , -27 , 81

∵ a_{1} = 1

∵ a_{2} = -3

∴ r=\frac{-3}{1}=-3

∵ a_{2} = -3

∵ a_{3} = 9

∴ r=\frac{9}{-3}=-3

∵ a_{3} = 9

∵ a_{4} = -27

∴ r=\frac{-27}{9}=-3

∵ a_{4} = -27

∵ a_{5} = 81

∴ r=\frac{81}{-27}=-3

∵ All the ratios above are equal -3

∴ The sequence is a geometric sequence

The sequence -7 , -5.8 , -4.6 , -3.4 , -2.2 is not a geometric sequence

Learn more:

You can learn more about the geometric sequence in brainly.com/question/1522572

#LearnwithBrainly

lorasvet [3.4K]3 years ago
3 0

Answer b ok ok ok

ok ok ok

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Step-by-step explanation:

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Step-by-step explanation:

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Of the cars sold during the month of July, 89 had air conditioning, 99 had an automatic transmission, and 74 had power steering.
DedPeter [7]

Answer:

There are a total of 23 cars with air conditioning and automatic transmission but not power steering

Step-by-step explanation:

Let A be the cars that have Air conditioning, B the cars that have Automatic transmission and C the cars that have pwoer Steering. Lets denote |D| the cardinality of a set D.

Remember that for 2 sets E and F, we have that

|E \cup F| = |E| + |F| - |E \cap F|

Also,

|E| = |E ∩F| + |E∩F^c|

We now alredy the following:

|A| = 89

|B| = 99

|C| = 74

|A \cap B \cap C| = 5

|(A \cup B \cup C)^c| = 24

|A \ (B U C)| = 24 (This is A minus B and C, in other words, cars that only have Air conditioning).

|B \ (AUC)| = 65

|C \ (AUB)| = 26

|B \cap C| = 11

We want to know |(A∩B) \ C|. Lets calculate it by taking the information given and deducting more things

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99 = |B| = |B ∩ C| + |B∩C^c| = 11 + |B∩C^c|

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