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2 years ago

How do you find the first five terms of a sequence defined recursively

1 answer:

6 0

Interesting question. Good to know for computer science.
Suppose you have a function like
an = 3x - 2 Try the first couple
a1 = 3(1) - 2
a1 = 3 - 2
a1 = 1

a2 = 3(2) - 2
a2 = 6 - 2
a2 = 4 So each term differs by 3
a2 - a1 = 3

an = a_(n - 1) + 3
a3 = a2 + 3
a3 = 4 + 3
a3 = 7

a4 = a3 + 3
a4 = 7 + 3
a4 = 10

a5 = a4+ 3
a5 = 10 + 3
a5 = 13

I'll do one more and then check it.
a6 = a5 + 3
a6 = 13 + 3
a6 = 16

a6 = 3x -2
a6 = 3*6 - 2
a6 = 18 - 2
a6 = 16 which checks.

So the general formula is
an = a_(n - 1) * k if you were multiplying or
an = a_(n - 1) + k if you were adding. The key thing is that you are working with the previous term.

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Can someone please help me.

Art [367]

I will give you everything I can do:

11)

Lets say Car A travels at x mph. That means Car B travels at x+2 mph.

Both of them are traveling towards each others, so we can say the total speed is 2x+2.

Now i takes 3 hrs and we know the distance.

Since R*T=D

Then 3(2x+2)=270

So 2x+2=90

2x=88

x=44

12)

To find perpendicular we want to find the opposite reciprocal of the original slope. Therefore the slope is 3/2.

Now we must find the equation of the line with the given variable.

First find b.

5=3/2*4+b

b = -1

So the equation of this line is:

y=3/2x-1

13) All work will be shown below.

6-3(-2-4x)=2(3(x-4)+7)

6+6+12x=2(3x-12+7)

12+12x=2(3x-5)

12+12x=6x-10

6x=-2

x = -1/3

14)

First we must find the amount each train traveled.

The speed of F train(Freight train)=x

The speed of P train(passenger train)=x+6

Their combined speed is 2x+6

It takes 2 hrs to cover 100 miles

So 2(2x+6)=100

2x+6=50

2x=44

x=22

So the freight train covered 44 miles and the passenger train covered 56 miles.

To find average speed you must do Total Distance/Total Time.

44/2 and 56/2

Which are 22 and 28.

The average speed of F train is 22 mph and average speed of P train is 28 mph.

15) Again opposite reciprocal.

3/5 -> -5/3

Work:

-4=-3*-5/3+b

-4=5+b

b=-9

y = -5/3x-9

16)

F=kx-kx0

First kx0 = 0

So F=kx

So x=F/k

4 0

3 years ago

Fill in the blanks with the answer to each question based on information provided.Two toy robots are having a race. Robot A can

GalinKa [24]

Answer:

1 1/14 seconds
4 2/7 seconds

Step-by-step explanation:

We are being asked for times, so we can express the rate in terms of seconds per meter.

(15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter

1) It will take Robot A 1 1/14 seconds to go 1 meter.

2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)

5 0

2 years ago

8m + 5n for m= 3 and n=-5

sasho [114]

Answer:

- 1

Step-by-step explanation:

8m + 5n

8(3) + 5(- 5)

24 + (- 25)

24 - 25

- 1

6 0

2 years ago

Read 2 more answers

Write a system of equation.

Alecsey [184]

Luis spent $9.50, in which:

Candy (y) = $1.25

Chips (x) = $0.50

$9.50 = 1.25y + 0.50x

Luis bought 10 snacks in all

10 = x + y

-----------------------------------------------------------------------------------------------------------------

You're answer:

x + y = 10

1.25y + 0.50x = 9.50

-------------------------------------------------------------------------------------------------------------------

hope this helps

7 0

3 years ago

In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?

Marina86 [1]

we have

$6 = x^{2}- 10x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2}- 10x+25=6+25$

$x^{2}- 10x+25=31$

Rewrite as perfect squares

$(x-5)^{2}=31$

$(x-5)=(+/-)\sqrt{31}\\ x1=5+\sqrt{31} \\ x2=5-\sqrt{31}$

therefore

the answer is

the solutions are

$x1=5+\sqrt{31} \\ x2=5-\sqrt{31}$

7 0

2 years ago

Read 2 more answers