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3 years ago

What is the recursive formula for this geometric sequence?–2, –16, –128, –1024, ...

Mathematics

1 answer:

Tatiana [17]3 years ago

5 0

Answer:

$b_n=-2\cdot 8^{n-1}$

Step-by-step explanation:

Denote first four terms of the geometrc sequence as

$b_1=-2,\\ \\b_2=-16,\\ \\b_3=-128,\\ \\b_4=-1024.$

Note that

$b_2=b_1\cdot q\Rightarrow -16=-2\cdot 8;\\ \\b_3=b_2\cdot q\Rightarrow -128=-16\cdot 8;\\ \\b_4=b_3\cdot q\Rightarrow -1024=-128\cdot 8.$

Then the common ratio is

$q=8.$

Therefore, the recursive formula for the geometric sequence is

$b_n=b_1\cdot q^{n-1}\Roghtarrow b_n=-2\cdot 8^{n-1}.$

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4. If the paint costs $30 per gallon and you need to spend $60 on supplies, and you can

Bezzdna [24]

Step-by-step explanation:

if I understand this right, then you need paint and additional supplies.

but I don't see any information indicating how many gallons of paint I will need.

so, I can go only with the 1 gallon specified.

so,

1×30 + 60 = $90

we can save $45 per month.

then we need

90 / 45 = 2

months to have enough money.

please update the numbers to how many gallons you really need, and then take that result and divide it by the 45 savings per month.

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3 years ago

Erin and dan went shopping at their local store. Erin bought shirts that cost $12 each and spent $18 on accessories. Dan bought

andrezito [222]

Answer:

Step-by-step explanation:

I think below is your full question:

Erin and Dan went shopping at their local store. Erin bought shirts that cost $12 each and spent $18 on accessories. Dan bought the same number of shirts as Erin for $16 each and spent $10 on accessories.

If Erin and Dan were billed the same amount by the store, how many shirts did each of them buy?

Here is my answer

Let x is number of shirts

Person COST

ERIN 12x+18

DAN 16x+10

Equally Billed 12x+18=16x+10 <=> x = 2

so each of them buy 2 shirts

7 0

4 years ago

5c + 3 ≥ 6x -8 Solve the following inequality for cc. Write your answer in simplest form.

irina [24]

Answer:

c≥2(x-2) ÷ 5

Step-by-step explanation:

5c+3≥6x-8

5c ≥6x-8-3

5c≥6x-12

c≥(6x-12) ÷ 5

c≥ 2(x-2) ÷5

3 0

3 years ago

Find the average rate of change of the function from x=1 to x=2. f(x)=−14/x^2

Irina-Kira [14]

Answer:

The average rate of change of the function from x=1 to x=2 will be: 10.5

Step-by-step explanation:

Given the function

$f\left(x\right)=-\frac{14}{x^2}$

at x₁ = 1,

f(x₁) = f(1) = -14/(1)² = -14/1 = -14

at x₂ = 2,

f(x₂) = f(2) = -14/(2)² = -14/(4) = -3.5

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate of change = [f(x₂) - f(x₁)] / [ x₂ - x₁]

= [-3.5 - (-14)] / [2 - 1]

= [-3.5 + 14] / [1]

= 10.5 / 1

= 10.5

Therefore, the average rate of change of the function from x=1 to x=2 will be: 10.5

6 0

3 years ago

Discussion Prompt: A fair coin is tossed twice and the number of heads is recorded. Jose says the P(1 head) = 1/2, while Jeff st

NemiM [27]

Let H represent heads and T represent tails.

Writing HH means we get two heads and HT means we get heads first, then tails second, and so on.

We have these four possible outcomes when flipping two coins

Of those four outcomes, two of them have exactly one head show up (HT and TH). The probability of getting exactly one head is 2/4 = 1/2, so this is why Jose is correct.

8 0

3 years ago