All categories

2 years ago

Consider the sequence given by the formula a(n + 1) = 5a(n) and a(1) = 2 for n ≥ 1.

Mathematics

1 answer:

saw5 [17]2 years ago

3 0

Answer:

The formula means; a of the next arithmetic n equals to 5 multiplied by a of the preceding n knowing that a of when n=1 is 2 and n must be 1 or greater than 1.

Step-by-step explanation:

a(n + 1) = 5* a(n) for n≥1

given that

a(1) = 2

therefore:

when n = 1, a(2) = 5* a(1) = 5 * 2 = 10

when n = 2, a(3) = 5*a(2) = 5 * 10 = 50

The formula means; a of the next arithmetic n equals to 5 multiplied by a of the preceding n knowing that a of when n=1 is 2 and n must be 1 or greater than 1.

You might be interested in

The ordered pair D (-4,-2) has been plotted for you. If you reflected coordinate d over the x-axis, which point from part A woul

Serjik [45]

A= (-4,2)

The x value (-4) stays the same when reflected over the x-axis, so only the y-value gets reflected and therefore changed.
The resultant coordinate is (-4,2)

6 0

3 years ago

A study was conducted to investigate the relationship between the resale price, y (in hundreds of dollars), and the age, x (in y

GaryK [48]

Answer:

a. $121.07

b. $60.9

C. $20.03

Step-by-step explanation:

From the equation given

Y=181.7-20.21x

Where y is in dollars and X is in years

a. To find the resale price after 3years we have, we substitute x=3 into the given equation.

We have

y=181.7-20.21(3)

y=181.7-60.63

y=121.07

The resale price after 3years is $121.07

b. To find the resale price after 6years we have, we substitute x=6 into the given equation.

We have

y=181.7-20.21(6)

y=181.7-120.72

y=60.98

The resale price after 3years is $60.98

C. To find the average decrease per year, we have

[(x=3)-(x=6)]/3

=(121.07-60.98)/3

$20.03

Hence the average annual decrease is $20.03

8 0

2 years ago

Read 2 more answers

What is A if a is equal to 1

MA_775_DIABLO [31]

A would be equal to 1 since a is equal to one already

3 0

2 years ago

Read 2 more answers

Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the

Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

$y=Ce^{kt}$ . We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is $\frac{dy}{dt}$ . Thus, the change in the concentration of salt is found in

$\frac{dy}{dt}=$ inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

$3(\frac{y}{400})$