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4 years ago

Indicate a general rule for the nth term of this sequence. 6a, 3a, 0, -3a, -6a, . . .

Mathematics

2 answers:

Lesechka [4]4 years ago

8 0

6a-(n-1)(3a) is the nth term
Expanding we get 6a-3an+3a=9a-3an=3a(3-n)
SOLUTION: nth term is 3a(3-n)

Elza [17]4 years ago

4 0

Answer:

The answer is $a_n=6a-3a(n-1)$

Step-by-step explanation:

In order to determine the general rule, we have to identify the difference between each term. We have to subtract every two continuous terms:

$3a-6a=-3a\\0-3a=-3a\\-3a-0=-3a\\-6a-(-3a)=-6a+3a=-3a$

Then, we know that we have to subtract -3a to every next term. The first term of the sequence is 6a and after that we have to subtract -3a since the second to the nth term.

Thus the nth term of the sequence is:

$a_n=6a-3a(n-1)$

To check the expression:

$n=1\\a_1=6a-3a(1-1)=6a-3a(0)=6a\\\\n=3\\a_3=6a-3a(3-1)=6a-3a(2)=6a-6a=0$

So, the expression is right.

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Bo and Brica are yoga instructors. Between the both of them, they teach 46 yoga classes each week. If Brica teaches 11 fewer tha

PtichkaEL [24]

Bo teaches 19 classes and Brica teaches 27 classes per week

Step-by-step explanation:

Bo and Brica are yoga instructors

They teach 46 yoga classes each week
Brica teaches 11 fewer than twice as many as Bo

We need to find how many classes each instructor teaches per week

Assume that Bo teaches x classes per week

∵ Bo teaches x classes per week

∵ Brica teaches 11 fewer than twice as many as Bo

∵ Twice means times 2 and 11 fewer is - 11

- Multiply x by 2 and subtract 11 from the product

∴ Brica teaches 2x - 11 classes per week

∵ They teach 46 classes per week

- Add the number of their classes and equate the sum by 46

∴ x + 2x - 11 = 46

- Add the like terms in the left hand side

∴ 3x - 11 = 46

- Add 11 to both sides

∴ 3x = 57

- Divide both sides by 3

∴ x = 19

∵ Bo teaches x classes per week

∴ Bo teaches 19 classes per week

∵ Brica teaches 2x - 11 classes per week

∴ Brica teaches 2(19) - 11 = 27 classes per week

Bo teaches 19 classes and Brica teaches 27 classes per week

Learn more:

You can learn more about the linear equations in brainly.com/question/11306893

#LearnwithBrainly

5 0

3 years ago

Writing to explain what are compatible numbers? What compatible numbers would you pick to estimate the diferrent of 777-248? Why

Sphinxa [80]

Compatible numbers are rounded numbers. the compatible number for 777 is 800 , and the compatible number for 248 is 200 because I rounded to the nearest hundreds place

I hope I helped you!!!!<3

8 0

3 years ago

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The d

kozerog [31]

Answer: 49.85%

Step-by-step explanation:

Given : The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped ( normal distribution ) and has a mean of 61 and a standard deviation of 9.

i.e. $\mu=61$ and $\sigma=9$

To find : The approximate percentage of lightbulb replacement requests numbering between 34 and 61.

i.e. The approximate percentage of lightbulb replacement requests numbering between 34 and $34+3(9)$ .

i.e. i.e. The approximate percentage of lightbulb replacement requests numbering between $\mu$ and $\mu+3(\sigma)$ . (1)

According to the 68-95-99.7 rule, about 99.7% of the population lies within 3 standard deviations from the mean.

i.e. about 49.85% of the population lies below 3 standard deviations from mean and 49.85% of the population lies above 3 standard deviations from mean.

i.e.,The approximate percentage of lightbulb replacement requests numbering between $\mu$ and $\mu+3(\sigma)$ = 49.85%

⇒ The approximate percentage of lightbulb replacement requests numbering between 34 and 61.= 49.85%

4 0

3 years ago

The coffee shop owner explains that she will work 12 hours more than you do if you get the job. She will work 50 hours edch week

MrMuchimi

Answer:

The owner says that she will work 12 hours more than you if you get the job.

We know that she works 50 hours each week.

then, knowing that she works 50 hours per week and that she works 12 hours more than you, you have that, if H is the number of hours that you work per week, you have:

H + 12 = 50

Here says that the number of hours that you work, plus 12 hours, is equal to the number of hours that the owner works.

H = 50 - 12 = 38

This means that you would work 38 hours per week.

3 0

3 years ago

Deposit $500 4% interest 2 years

STatiana [176]

Are you looking for the amount after interest gained? If so I believe the answer would be $40.

500 x 0.04 x 2 = 40

7 0

3 years ago