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3 years ago

Determine if the sequence is arithmetic. If it is, find the common difference.

Mathematics

1 answer:

mr_godi [17]3 years ago

7 0

Answer:

In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.

So we just need to take different pairs of consecutive terms and see if their difference is always the same:

1) The differences are:

32 - 35 = -3

29 - 32 = -3

26 - 29 = -3

So yes, this is an arithmetic sequence and the common difference is -3

2) The differences are:

-23 - (-3) = -20

-43 - (-23) = -20

-63 - (-43) = -20

This is an arithmetic sequence, and the common difference is -20

3) The differences are:

-64 -(-34) = -30

-94 -(-64) = -30

-124 -(-94) = -30

This is an arithmetic sequence and the common difference is -30

4) The differences are:

-40 -(-30) = -10

-50 - (-40) = -10

-60 - (-50) = -10

This is an arithmetic sequence and the common difference is -10

5) The differences are:

-9 - (-7) = -2

-11 - (-9) = -2

-13 - (-11) = -2

This is an arithmetic sequence, and the common difference is -2

6) The differences are:

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

This is an arithmetic sequence, and the common difference is 5.

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For a certain candy, 20% of the pieces are yellow, 15% are red, 20% are blue, 20% are green, and the rest are brown. a

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Answer:

Step-by-step explanation:

Based on the question we are given the percentages of each of the types of candies in the bag except for brown. Since the sum of all the percentages equals 75% and brown is the remaining percent then we can calculate that brown is (100-75 = 25%) 25% of the bag. Now we can show the probabilities of getting a certain type of candy by placing the percentages over the total percentage (100%).

Brown: $\frac{25}{100}$
Yellow or Blue: $\frac{20}{100} +\frac{20}{100} = \frac{40}{100}$ ....add the numerators

Not Green: $\frac{80}{100}$ .... since the sum of all the rest is 80%

Stiped: $\frac{25}{100}$ .... there are 0 striped candies.

Assuming the ratios/percentages of the candies stay the same having an infinite amount of candy will not affect the probabilities. That being said in order to calculate consecutive probability of getting 3 of a certain type in a row we have to multiply the probabilities together. This is calculated by multiplying the numerators with numerators and denominators with denominators.