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ra1l [238]
2 years ago
5

Given a2 = 15 and a5= -3,240 of a geometric sequence, what is the recursive equation for the nth term

Mathematics
1 answer:
Assoli18 [71]2 years ago
6 0

Answer:

  a[1] = -5/2

  a[n] = -6·a[n-1]

Step-by-step explanation:

The explicit formula for the n-th term is ...

  an = a1(r^(n-1))

We can use this to find the common ratio, r.

  a2 = 15 = a1·r^(2-1) = a1·r

  a5 = -3240 = a1·r(5-1) = a1·r^4

Dividing the second equation by the first gives ...

  -3240/15 = (a1·r^4)/(a1·r)

  -216 = r^3 . . . . simplify

  -6 = r . . . . . take the cube root

The first term is ...

  15 = a1·(-6)

  a1 = 15/-6 = -5/2

__

The entire recursive formula for the sequence is ...

  a[1] = -5/2 . . . . . . . . . . the initial condition

  a[n] = -6·a[n-1] . . . . . . the recursion relation

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Solve the following system of equations graphically on the set of axes below.<br> Y=1/3x+6 y=-5/3x-6
Aleks [24]

Answer:

I can not solve it in the system of the image, but i will give you the graph so you can copy it, or at least see how it is done.

First, we have the lines:

y = (1/3)*x + 6

y = (-5/3)*x - 6

To graph these lines, you must find two points for the lines and then draw a line that connects the points.

To do it, you can evaluate each line in two different values of x, for example for the first line we can have:

y(0) = (1/3)*0 + 6 = 6   (then we have the point (0, 6))

y(3) = (1/3)*3 + 6 = 7    (then we have the point (3, 7))

And for the second line, we will have:

y(0) = (-5/3)*0 - 6 = -6 (then we have the point (0, -6))

y(3) = -(5/3)*3 - 6 = -11 (then we have the point (-3, -11))

Now with those points we can graph the lines, and the solution of the system of equation will be the point where the two lines intersect.

The graphs of the lines are shown below:

Where the grey line is the first one, and the green is the second.

In the graph, you can see that the lines intersect in the point (-6, 4)

Then the solution for the system is x = -6, and y = 4.

6 0
3 years ago
Suri makes $15 per hour and gets a weekly bonus of $25. Juan makes $14 per hour and gets a weekly bonus of $50. Is it possible f
Papessa [141]

Answer:

Yes. Suri and Juan can make the same amount of wages by working 25 hours in one week.

Step-by-step explanation:

Let each of them work x hours per week.

Suri makes $15 per hour, so in x hours Suri will make $ 15x. The total wages per week for Suri will be:

Total Wages = y = 15x + Bonus = 15x + 25

Juan makes $14 per hour, so in x hours Juan will make $ 14x. The total wages per week for Juan will be:

Total Wages = y = 14x + Bonus = 14x + 50

If they will make the same wages, their wages must be equal, i.e.

15x + 25 = 14x + 50

15x - 14x = 50 - 25

x = 25

This result shows us that if Suri and Juan work for 25 hours per week they will make the same amount of wages.

7 0
3 years ago
There are 40 animals at a petting zoo, all of which are goats or rabbits, and each animal is either an adult or a child. There a
Natali5045456 [20]
Total number of animals: 40
Types of animals: 4
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Adult rabbits: 2x
Child goats: 3x
Child rabbits: 2x

x+2x+3x+2x = 40
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x = 5
There are 5 adult goats.

The correct answer is 5 adult goats.
8 0
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klio [65]
The function h is defined by h(x)=x^2 +2.
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satela [25.4K]

20

Step-by-step explanation:

5x4

8 0
3 years ago
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