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2 years ago

What is the explict rule for the sequence 12,22,32,42

Mathematics

1 answer:

icang [17]2 years ago

8 0

The explicit rule for given sequence is:

$a_n=2+10n$

Further explanation:

We have to determine first of all if the sequence is arithmetic or geometric.

If the difference of two consecutive terms is same then the sequence is arithmetic sequence
If the ratio of two consecutive terms is same then the sequence is geometric sequence

Given sequence is:

12,22,32,42

$a_1=12\\a_2=22\\a_3=32\\.......\\Let\\d=Common\ difference\\d=a_2-a_1=22-12=10\\d=a_3-a_2=32-22=10$

The common difference is 10 which is same for all consecutive terms. So the sequence is an arithmetic sequence.

The general formula for arithmetic sequence is:

$a_n=a_1+(n-1)d\\Here,\\a_n\ is\ the\ nth\ term\\a_1\ is\ the\ first\ term\\d\ is\ the\ common\ difference$

Putting the values of a1 and d

$a_n= 12+(n-1)(10)\\a_n=12+10n-10\\a_n=2+10n$

The explicit rule for given sequence is:

$a_n=2+10n$

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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Write a real-world problem that is solved by an equation and then solve (show work).

ololo11 [35]

A company is selling books. It has to pay $500 to start printing the books, and once they have done that, the books sell at $14.99 each. How many books must they sell to make a profit?

First we would model an equation. X will be the amount of books sold, and Y will be profits (in dollars obv). They had to pay $500 before they could start selling, so we must account for that too.

This equation would be $y=14.99x-500$ because for every book sold, X increases by 1, increasing Y by 14.99

The answer would be 34 books sold in order to turn a profit. (500/14.99=

6 0

2 years ago

Will give brainliest

ehidna [41]

Answer:

25.047 or roughly 25.

Step-by-step explanation:

I solved it wrong the first time then i double check with wolframalpha and got the correct number.

We know that the area of the tile is 18 $\sqrt{3}$ and it makes a triangle, we also know the base and height. In this case the base is 2 $\sqrt{3}^{x/12}$ and the height is also given which is $\sqrt{3}^{\frac{x}{6} }$ .

Area of triangle = $\frac{bh}{2}$ ,

substituting we will end up with 18 $\sqrt{3}$ =( 2 $\sqrt{3}^{x/12}$ * $\sqrt{3}^{\frac{x}{6} }$ ) / 2

Here is the tricky part $\sqrt{x} = x^{\frac{1}{2} }$ , i totally forgot about that lol.

Simplifying: we will get 18 $\sqrt{3}$ = $3^{\frac{x}{8} }$

Now, in order to find the x, we will need to take the log of both sides.

$log18\sqrt{3} = \frac{x}{8} log3$

Solving for x we end up getting:

$8\frac{log18\sqrt{3} }{log3}$ = x

where x = 25.047.

To be honest I deserve a nobel prize not a brainliest lol.

Good question bro, take it easy.

5 0

2 years ago

-3x + 5y = -6<br> 6x - 10y = 12

enyata [817]

Answer:

1. Let's solve for x.

−3x+5y=−6

Step 1: Add -5y to both sides.

−3x + 5y + −5y = −6 + −5y

−3x = −5y − 6

Step 2: Divide both sides by -3.

−3x

−3

−5y−6

−3

y+2

2. Let's solve for x.

6x−10y=12

Step 1: Add 10y to both sides.

6x−10y+10y=12+10y

6x=10y+12

Step 2: Divide both sides by 6.

10y+12

y+2

7 0

3 years ago

A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population tha

galben [10]

Answer: Therefore, Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Number of population = 132000

Number of voting districts = 11

According to question, no district is to have a population that is more than 10 percent greater than the population of any other district.

Let the number of population that the least populated district could have be 'x'.

So, it becomes,

$x+10(1.1x)=132000\\\\x+11x=13200\\\\12x=132000\\\\x=\dfrac{132000}{12}\\\\x=11000$

Hence, there are 11000 population that the least populated district could have.

Therefore, Option 'D' is correct.

4 0

3 years ago

Fizzbos sells only sandwiches. They offer five choices of bread, five types of meat toppings, four types of cheese and eight veg

sineoko [7]

Answer:

<em>800 possible combinations</em>

Step-by-step explanation:

We can reach the answer by simple logic reasoning. Knowing Fizzbos' sandwiches have one type of bread, one meat, one type of cheese and one vegetable for their sandwiches, we can find the possible combinations like this:

We have 5 choices of bread, there are, of course, 5 different kinds of sandwiches to offer.

We also know there are 5 types of meat toppings which, combined with the 5 possible choices we already have, will make

5*5 possible combinations

Now we consider the 4 types of cheese combined with our previous kinds of sandwiches to get

5*5*4 possible combinations

Finally, we have 8 vegetable toppings, making our final result

5*5*4*8 = 800 possible combinations

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3 years ago

What is the explict rule for the sequence 12,22,32,42​

What is the explict rule for the sequence 12,22,32,42