MATHEMATICS HIGH SCHOOL

2. Which is larger?The common ratio, r , in a geometric sequence whose second term is
24 and whose fifth term is 1536
or
The common difference, d , in an arithmetic sequence whose fourth
term is 16 and whose seventh term is 31.

Answers

Answer 1
Answer:

Answer:

The common difference d is larger than the common ratio r

Step-by-step explanation:

  • The common difference in the arithmetic sequence  d=u_(n)-u_(n-1)
  • The nth term in the arithmetic sequence is a_(n)=a+(n-1)d , where a is the first term
  • The common ratio in the geometric sequence r=(u_(n))/(u_(n-1))
  • The nth term in the geometric sequence is a_(n)=a(r)^(n-1) , where a is the first term

Geometric sequence

∵ The second term is 24

∴ u_(2) = 24

∵ u_(2)=a(r)^(2-1)=ar

- Equate it by its value

∴ ar = 24 ⇒ (1)

∵ The fifth term is 1536

∴  u_(5) = 1536

∵ u_(5)=a(r)^(5-1)=ar^(4)

- Equate it by its value

∴ ar^(4) = 1536 ⇒ (2)

Divide (2) by (1)

∴ (ar^(4))/(ar)=(1536)/(24)

- Divide up and down by ar

∴ r³ = 64

- Take ∛  for both sides

∴ r = 4

Arithmetic sequence

∵ The fourth term is 16

∴ u_(4) = 16

∵ u_(4) = a + (4 - 1)d

∴ u_(4) = a + 3 d

- Equate it by its value

∴ a + 3d = 16 ⇒ (1)

∵ The seventh term is 31

∴ u_(7) = 31

∵ u_(7) = a + (7 - 1)d

∴ u_(7) = a + 6 d

- Equate it by its value

∴ a + 6 d = 31 ⇒ (2)

Subtract equation (1) from equation (2) to eliminate a and find d

∵ (a - a) + (6 d - 3 d) = (31 - 16)

∴ 3 d = 15

- Divide both sides by 3

∴ d = 5

∵ r = 4 and d = 5

∴ d > r

∴ The common difference d is larger than the common ratio r

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Apply the commutative property to 13×7×21 to rearrange the terms and still get the same solution

Answers

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-4(x+5)=-4x-20 how do you answer it

Answers

Answer:

0

Step-by-step explanation:

-4x-20=-4(x+5)

-4x-20=-4x-20

0=0

One in ten plus one. how much is it?

Answers

1 In 10 is a ratio 1:10 or 1/10. Add 1 for

1 + 1/10 = 1 1/10

Is 1 a irrational number

Answers

Answer:

1 is not an irrational number, it is rational

Step-by-step explanation:

The estimated snowfall for a local city is 6.75 inches. The actual snowfall was 10.25 inches. What is the percent error for the amount of snowfall

Answers

Answer: ~ 34.15%

Step-by-step explanation:

To calculate the percent error for the amount of snowfall, you can use the following formula:

Percent Error = [(|Estimated Value - Actual Value|) / Actual Value] * 100%

In this case, the estimated snowfall is 6.75 inches, and the actual snowfall is 10.25 inches. Plugging these values into the formula:

Percent Error = [(|6.75 - 10.25|) / 10.25] * 100%

Percent Error = [(3.5) / 10.25] * 100%

Percent Error ≈ 34.15%

So, the percent error for the amount of snowfall is approximately 34.15%. This means that the estimated snowfall was about 34.15% lower than the actual snowfall.
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