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2 years ago

What is the recursive formula for the geometric sequence with this explicit formula?

Mathematics

1 answer:

IRINA_888 [86]2 years ago

5 0

For the given geometric sequence, we have:

$a_1 = 9\\\\a_n = (-1/3)*a_{n-1}$

So the correct option is B.

<h3>Which is the recursive formula?</h3>

Here we have the geometric sequence:

$a_n = 9*(-\frac{1}{3} )^{(n - 1)}$

To get the initial value of the geometric sequence, we just need to replace n by 1, so we get:

$a_1 = 9*(-\frac{1}{3} )*(1 - 1) = 9$

Now, notice that the common ratio is (-1/3), this means that each term of the sequence is (-1/3) times the previous term.

$a_n = (-1/3)*a_{n-1}$

Then the correct option is B.

If you want to learn more about geometric sequences:

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You might be interested in

An arena receives $1,700 per event for 12 concerts. If the costs for this sponsorship total $14,000, what is the profit margin f

miss Akunina [59]

Answer:

total profit margin for all 12 concert is $6,400.

profit margin for all one concert is $533.33

Step-by-step explanation:

Amount of money received for one event = $1700

Total no of concert = 12

Total money received for 12 event = Amount of money received for one event * Total no of concert

Total money received for 12 event = $1700 *12 = $20,400

Total cost of sponsorship = $14,000

Profit margin is the difference money invested and money earned.

here total investment is $14,000

Total money earned is $20,400

Therefore profit margin = money earned - total investment

= $20,400 - $14,000 = $6,400

Therefore total profit margin for all 12 concert is $6,400.

However to calculate profit margin for one concert we can simply divide the total profit margin for all 12 concert by no of concert (i.e 12)

profit margin for one concert = total profit margin for all 12 concert/total no of concert = $6,400/12 = $533.33

profit margin for all one concert is $533.33

6 0

3 years ago

What is (2-2i√3)4 equivalent to?

maxonik [38]

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

<h3>What are complex numbers?</h3>

Complex numbers are numbers of the form z = x + iy

<h3>a. Complex numbers in polar form</h3>

Complex numbers in polar form z = r(cosθ + isinθ) where

r = √(x² + y²) and
θ = tan⁻¹(y/x)

Given that z = (2 - 2i√3)⁴ =

So,

x = 2 and
y = -2√3

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

<h3>Powers of complex numbers</h3>

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

<h3>b. Complex numbers in rectangular form</h3>

The complex number z = r(cosθ + isinθ) in rectangular form is z = x + iy where

x = rcosθ and
y = rsinθ

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y = rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

Learn more about complex numbers in polar form here:

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7 0

2 years ago

if one store is selling 3/4 of a bushel of apples for 9 dollars and another store is selling 2/3 of a bushel of a apple for 9 do

fredd [130]

3/4 of a bushel is 75%, 2/3 of a bushel is 66.67% about. Being that both cost $9 the first store who is selling 3/4 of a bushel is a better deal because you get more for what you pay for.

8 0

3 years ago

A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:

Sedaia [141]

Answer:

Time:

Car > Truck > Boat.

Cost of produce:

Truck > Boat > Car

Profit

Car > Truck > Boat.

We know that a worker works 400 minutes each day, and the profit that each worker needs to generate is $35, let's find how each worker needs to spend their time.

Let's call T to the number of trucks he makes, C for cars and B for boats.

Then, if he works 400 minutes we have:

T*10 + C*12 + B*8 ≤ 400

this means that the time expended crafting the toys can be, at most, 400 minutes (here you use the inequality because the worker actually can be less effective than the max, maybe tacking a break or something like that)

The other equation is:

T*1 + C*1.5 + B*0.6 ≥ 35

Here we use the inequality because the profit needs to be at least 35$, none the less, the profit can be more than tath.

Notice that if we want to solve the system with for the equal signs, it is:

T*1 + C*1.5 + B*0.6 = 35

T*10 + C*12 + B*8 = 400

We have 3 variables and 2 equations, this means that there are more than one solution for this system.

6 0

3 years ago

Help me please on the wrong answers (C means correct)

yan [13]

The answer for 3 is 5 7/8

7 0

4 years ago

Read 2 more answers