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Serga [27]
3 years ago
15

What are the next three terms of the following sequence?

Mathematics
2 answers:
kaheart [24]3 years ago
5 0

we know that given terms were i geometric progression.

which means common ratio is same between two consecutive terms .

here we have 8,40,200,1000.

we know that common ratio =second term/first term =40/8=5.

so each and every terms is multiplied by 5 to get next term for this series the term after 1000 is 5000 =1000*5.

in part b we have another series which is having common ratio of -2.

so we need to multiply with -2 to find next term.

80*(-2)=-160.

for part c the common ratio is -2 .

so we need to multiply with -2 *previous term =-2*16 =-32.

mariarad [96]3 years ago
4 0

We can see first sequence :

40/8 = 5

200/40 = 5

1000/200 = 5

this implies it is a geometric sequence with common ratio r= 5 and first term a= 8

every next term can be achieved by multiplying 5 to previous term

5th term = 1000 * 5 = 5000

6th term = 5000 * 5 = 25000

7th term = 25000 * 5 = 125000

LEt us work on next one : 20/-10 = -2 , -40/20 = -2 80/-40 = -2

5th term : 80 *(-2) = -160

6th term : -160* -2 = 320

7th term = 320*-2 = -640

next is : 4/-2 = -2 -8/4 = -2 16/-8 = -2

5th term = 16 *- 2= -32

6th term = - 32*-2 = 64

7th term = 64*-2 = -128

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Step-by-step explanation:

Hey there!

Follow the steps to get answer.

  • Use one point formula and find 1st equation.
  • After that you find the slope of second equation.
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  • Put slope value of equation in equation (i) and simplify them to get equation.

The equation of a line passing through point (2,3) is;

(y-3)= m1(x-2).......(i).

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y =  \frac{ - 1}{2} x +  \frac{2}{3}

2nd equation..

Now, From equation (ii)

We have;

Comparing equation (ii) with y = mx+c.

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Slope = -1/2.

For perpendicular lines,

m1 \times m2 =  - 1

m1 \times  \frac{ - 1}{2}  =  - 1

Therefore the slope is 2.

Put value of slope (m1) in equation (i). We get;

(y - 3) = 2(x - 2)

Simplify them to get equation.

(y - 3) = 2x - 4

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Therefore the required equation is y = 2x-1.

<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em>

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3 years ago
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Answer:

210=75x-10x+35

Step-by-step explanation:

So we know to total profit he made is 210 dollars, in which he earned from 3 independent reasons.

The profits he made in per appointment will need a variable because we don't know how many appointments he made. So knowing that we can conclude that 75 dollars and 10 dollars per appointment has to have a variable after it. The same variable as well because both of which are money.

As of the tip, we don't need a variable because it is a one time addtion, he recieved a total of 35 dollars after all of the appointments, so no need to know how many. We already know the total.

So that leaves us to write an equation. The total=$per appointment-fee per appointment+tip. Which becomes 210=75x-10x+35.

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Step-by-step explanation:

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