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vodomira [7]
3 years ago
6

which of the following is an arithmetic sequence? * –20, –25, –30, –35, –45, ... *–15.6, –12.9, –10.2, –7.5, –4.8, ... * 3.1, 6.

2, 12.4, 24.8, 49.6, ... * 7.2, 3.6, 1.8, 0.9, 0.45, ...
Mathematics
1 answer:
AveGali [126]3 years ago
5 0

Answer:

–20, –25, –30, –35, –45 is an arithmetic sequence.

Step-by-step explanation:

An arithmetic sequence is defined by

T_n=T_1+k(n-1)

where

T_n is the nth term of the sequence

T_1 is the first term of the sequence

k is the difference between consecutive terms.

To find which sequence is arithmetic, let us look at each of the options one by one.

Option 1: –20, –25, –30, –35, –45

It is clear that each next term in this sequence is 5 less than the previous; therefore, this is an arithmetic sequence, and k=-5,the formula is

T_n=-20+-5(n-1)

Option 2: -15.6,-15.9,-10.2,-7.5,-4.8...

In this sequence there is not any common difference between the terms, for example: -15.6--15.9=<u>0.3</u>,   -15.9--10.2=-<u>5.7</u>   -10.2--7.5=-<u>2.7</u>. Therefore, this not an arithmetic sequence.

Option 3: 3.1, 6.2, 12.4, 24.8, 49.9...

In this sequence there is not any common difference between the terms, for example: 6.2-3.1 =<u>3.1</u>,   12.4-6.2 =<u>6.2</u>, 24.8-12.4 =<u>12.4</u>. So, this is not an arithmetic sequence.

Option 4: 7.2, 3.6, 1.8, 0.9, 0.45....

This sequence also does not have any common difference between the consecutive terms, for example: 7.2-3.6=<u>3.6</u>, 3.6-1.8=<u>1.8</u>, 1.8-0.9=<u>0.9.</u> So this is also not an arithmetic sequence.

Thus only option 1 is the arithmetic sequence.

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Answer:

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Step-by-step explanation:

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A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s
yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

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0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

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-0.2*x^2 - x + 100 = 0

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x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2}  = \frac{1 \pm 9 }{-0.4}

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

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x = 20

then the average speed initially is 20 km/h

3 0
2 years ago
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