Mathematics High School

(look at screenshot)
Write an explicit rule and recursive rule for a geometric sequence with a second term of 6 and a third term of 12.

explicit:

recursive:

(look At Screenshot)Write An Explicit Rule And Recursive Rule For A Geometric Sequence With A Second

Answers

Answer 1

Answer:

Explicit : [tex]a_n=3(2)^{n-1}[/tex]

Recursive: a₁ = 1

                  [tex]a_n=a_{n-1}(2)[/tex]

Step-by-step explanation:

We have to write the recursive formula for the geometric sequence with second term 2 and third term 12.

Geometric sequence will be in the form of,

a, ar, ar², ar³,...........

Here, r = common ratio

a = first term of the sequence

Here, ar = 6 ------(1)

And ar² = 12 ------(2)

By dividing equation (2) by (1),

[tex]\frac{ar^2}{ar}=\frac{12}{6}[/tex]

r = 2

From equation (1),

a(2) = 6

a = 3

Recursive formula of a geometric sequence is given by,

a₁ = a

[tex]a_n=a_{n-1}(r)[/tex]

Therefore, for the given sequence,

a₁ = 1

[tex]a_n=a_{n-1}(2)[/tex]

Similarly, explicit formula of the geometric sequence is given by,

[tex]a_n=a_1(r)^{n-1}[/tex]

[tex]a_n=3(2)^{n-1}[/tex]

Related Questions

what's the volume of the cone​

Answers

Given:-

[tex] \bullet [/tex] Radius (r) of the cone is 3 ft.

[tex] \bullet [/tex] Height (h) of the cone is 9 ft.

To Find:-

The volume of the cone.

Solution:-

We know,

Formula of Volume of cone is [tex] \frac{1}{3} [/tex]πr²h

So, Volume of the cone = [tex] \frac{1}{3} [/tex] × [tex] \frac{22}{7} [/tex] × (3)² × 9

Volume of the cone = [tex] \frac{1}{3} [/tex] × [tex] \frac{22}{7} [/tex] × 3 × 3 × 9

Volume of the cone = [tex] \frac{22 \: × \: 3 \: × \: 3 \: × \: 9}{3 \: × \: 7} [/tex]

Volume of the cone = [tex] \frac{1782}{21} [/tex]

Volume of the cone = 84.86 cubic ft.

The volume of the cone is 84.86 cubic ft. [Answer]

24 divided by the product of 6 and 2

Answers

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The product of 6 and 2 is twelve and if you divide 24 by 12 the answer is 2

or

6 x 2 = 12  

24 ÷ 12 = 2

answer: 2

Please help me I’m not smart
and this test is due in one hour.

Answers

Answer:

the pitch of the sound

Step-by-step explanation:

because the speed stays the same and the echo has the same variables so i believe it is the pitch

HELP giving brainlest and extra points!!!!!

Answers

Answer: 4

Step-by-step explanation:

Lynn is helping her mother make dresses. Each dress takes 3 2/3 yards of fabric. They have one roll of fabric. There are 16 yards of fabric on a roll. What is the maximum number of dresses Lynn and her mother can make before having to buy a second roll of fabric? ​

Answers

Answer:

4 dress will be the max

Step-by-step explanation:

it is a division question

16 yards on a roll ÷ 3⅔ yards of fabric

16÷3⅔

16÷ 11/3

16*3/11

48/11

4.3636

Complete the statement. Round to the nearest hundredth if necessary.

40 oz = lb

Answers

40 oz= 2.5 lb

One pound (lb) =16 Ounces
40/16=2.5

Answer:

2 paunds is the answer this is simple math broski

Elizabeth has $680 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• She buys a new bicycle for $437.63.
• She buys 2 bicycle reflectors for $17.63 each and a pair of bike gloves for $18.11.
She plans to spend some or all of the money she has left to buy new biking outfits
for $35.19 each.
What is the greatest number of outfits Elizabeth can buy with the money that's left
over?

Answers

Answer: 5 outfits

Step-by-step explanation: 17.63x2=35.26

                                             437.63+35.26+18.11=491

                                              680-491=189

                                              189 divided by 35.19= 5 (rounded)

Im stuck on this question, can someone help:)

Answers

Answer:

A) 29 plants

B) $90.75

Step-by-step explanation:

A) Divide 79.75 by 2.75. It will give you the plant number.

B) Multiply 4 and 2.75 which should equal 11. Add that to 79.75.

Good Luck!!!!!!!

Reduce -56/-70 to lowest terms

•-2/3
•-4/5
•4/5
•8/10

Answers

4/5 is the right answer.....

Answer:

option c, 4/5

You know that you want some type of wood flooring. You found these options at the store.

Wood Laminate: $1.65
Engineered Wood: $4.09
Solid wood: $5.59

Calculate the total cost of each material to determine which ones you can afford.
Must show all work.

Answers

Answer:

how much wood do you need

What is the decimal form of -1 and 1/12?

Answers

Answer:

Step-by-step explanation:

1/12 = 0.0833

-1 = 0.000

couldn't write it out so i took a pic of it

Answers

Answer:

4th is the answer

Step-by-step explanation:

Answer:

the measure of <ABD = 1/2 the measure of <ABC is the answer :)

Step-by-step explanation:

Help! Ive been stuck on this for 2 days!

Answers

Answer:

range = 13

median = 23

mode = none

mean = 22

Step-by-step explanation:

Answer:

mean: 22

median: 23

mode: none

range: 13

Step-by-step explanation:

mean

the mean of a data set is the sum of all the terms divided by how many terms there is, so:

23 + 29 + 25 + 16 + 17 ÷ 5 = 22

median

the median of a data set is the middle number so we arrange in order:

16, 17,  23, 25, 29

23 is the middle, so that's the median

mode

the mode is the number that's repeated the most, there isn't any repeats, so there isn't a mode

range

The range is the lowest value (16) subtracted from the highest value (29)

29 - 16 - 13

hope this helps:)

find the value of x and y​

Answers

Answer:

x=4

y=7

Step-by-step explanation:

x=4 because the left and right sides are equal

the upper side should equal the bottom side

so y+5=12

y=12-5

y=7

Hi could some one please help me on this

Answers

Answer:

A

Step-by-step explanation:

The Pythagorean theorem only works for right triangles. A right triangle has one 90-deg angle. This triangle has no 90-deg angle, so it is not a right triangle, and the Pythagorean theorem does not work to solve it.

Answer: A

HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP

Answers

Answer:

A = 15 u²

Explanation:

according to the coordinates the triangles is right at the pair (2, -3)

the area of the triangle = height × base × 1/2

the height is the line passing through the pairs (-1, 6) and (2, -3)

h² = (2-(-1))²+(-3-6)²

h² = 3² + (-9)²

h² = 9 + 81

h² = 90

h = √90

the base is the line passing through the pairs (5, -2) and (2, -3)

b² = (2-5)²+(-3-(-2))²

b² = 3² + (-3+2)²

b² = 9 + 1

b² = 10

b = √10

A = h×b×1/2

A = √90×√10×1/2

A = √900×1/2

A = 30×1/2

A = 15 u²

Mr. Garcia deposited $2,500 in a new account at his bank.

The bank pays 6.5% interest compounded annually on this account.
Mr. Garcia makes no additional deposits or withdrawals.


Which amount is closest to the balance of the account at the end of 2 years?

A.$2,513.00

B.$2,662.50

C.$2,835.56

D.$2,825.00

Answers

Answer:

$2,825.00

Step-by-step explanation:

First, I found out what 6.5% of 2,500 is, so 6.5% x 2,500 = 162.5 . Then I did 162.5 x 2, which equals 325. I then added 325 to 2,500 and got 2,825.

Which survey question has the least amount of bias?
a. Why are vegetables good for you?
b. How many hours of sleep do you get?
C. Do you think the media has a negative role in politics?
d. Why are teen drivers dangerous?

Answers

“Why are vegetables good for you?” This is because the others are all opinionated questions.

A wheel has a diameter of 28 inches. What is the approximate distance around the outside of the wheel? Use 3.14 for pi.

Answers

Answer:

43.96

Step-by-step explanation:warning might be wrong

Find the angle with a tangent ratio of 0.9325.
a. 77°
b. 43°
C. 13°
d. 47°

Answers

Answer:

B = 43

Step-by-step explanation:

Answer:B

Step-by-step explanation:

What is the surface area of cereal box whose length , breath, and height are 20cm , 8cm,30cm ,also find its volume

Answers

Answer:

V = 4800 cm^3

SA = 2000 cm^2

Step-by-step explanation:

V = l x w x h

V = 20 x 8 x 30

V = 4800 cm^3

20 x 8 x 2 = 320 cm^2

20 x 30 x 2 = 1200 cm^2

8 x 30 x 2 = 480 cm^2

320 + 1200 + 480 = 2000 cm^2

Which are rational numbers check all that are true

Answers

Answer:

All of them except the second one and third one are true .

Answer:

1/3, 3, -1/3

Step-by-step explanation:

A rational number is a number that can be expressed with a fraction. In this case we have:

1/3 , 3 (all natural numbers are also rational: in fact for example 3 can be expressed with the fraction: 3/1) , -1/3

333/0 is not a rational number because the division is impossible

√3 is not rational because can’t be expressed with a fraction


(a) Simplify
3a + 7b - a + 4b

Answers

Answer:

2a+11b

Step-by-step explanation:

Need like terms!

3a-a

=2a

7b+4b

=11b

How do I find the measurement of Angle x?

Answers

Answer:

26°

Step-by-step explanation:

The angle 123° is on a straight line. All angles on a straight line add up to 180°, so the first thing you should do is subtract 123 from 180.

(180-123)

Now, your answer should be 57°, and that is equal to angle W.

You now know two angles. Angles in a triangle add up to 180°, too, so all you do now is the following:

97 + 57 = 154

180- 154 + 26

And there's your answer!

A bakery advertised a bag of cookies today for $3.99. Why did the bakery set the price at $3.99 instead of $4.00?

a The bakery needs to get rid of old cookies.
b The bakery wants to improve the reviews on that brand.
c Our brains tend to notice the first digit first.
d We may pay an extra penny at the register.

Answers

The answer is D because at the register they charge you an extra penny to even out the number

Hope this helps !!!

Answer:

C.

Step-by-step explanation:

If you think about it, it makes a little bit of sense. You pay $3.99 for the bag of cookies when the initial price was $4. To you, it sounds cheaper. But you're technically paying the same amount of cash as you would for the previous amount of cookies, as nobody in America keeps 99 cents in their pockets at all times, and 99 cents obviously rounds up to a dollar, so it's technically the same price as before. Overall, this would be essentially just a cheap marketing technique that they're using to get more money out of a larger group of people. If they're trying to get rid of old cookies, they wouldn't lower the price by just a cent, lowering the price by just a cent in order to improve the reviews might as well do the opposite, and paying an extra cent doesn't make much of a difference considering the old price.  So thus the answer is C.

Have a good rest of your day.

Evaluate each expression for n = 5. 6n + n2​

Answers

Answer:

40

Step-by-step explanation:

1. Plug in the given value for n

6(5) + (5)2

2. Solve using PEMDAS

(I'm not sure if the 2 after the n is supposed to be squared, but if it was n^2 then the correct answer would be 55, I think)

30 + 10 = 40

Therefore, the answer is 40

Hope this helps :)

a. A person's height is positively associated with their arm span (the distance between the
ends of the fingertips as arms are held out on each side of the body). One of the tallest
men in history had an arm span measuring 7 inches more than his height. The combined
total of his arm span and height was 221 inches. How tall was this man?

Answers

Answer:

I didn't Sanderstead sorry

Please answer.

No links, no fake answers please

Answers

Answer:

The length of the side JH is approximately 31.5 feet long.

Step-by-step explanation:

There is a trigonometry law called the law of sines, which states the sine of an angle divided by its opposite side is equivalent to the sine of all the other angles in that right triangle divided by its corresponding opposite side. You can use this law to help you solve for x. By applying the law of sines, you'll get that [tex]\frac{sin(90^{o})}{88} =\frac{sin(21^{o})}{x}[/tex] ⇒ [tex]\frac{88}{sin(90^{o})} =\frac{x}{sin(21^{o})}[/tex] ⇒ [tex]x = \frac{88*sin(21^{o})}{sin(90^o)}[/tex] ⇒ [tex]x=31.5ft.[/tex]

Helppppppnowwwwwwwwwwwwww

Answers

Answer:

X=58

Step-by-step explanation:

Good luck .

Hope this helps u ;)

Can I get help with these three

Answers

Answer:

b is the answer

Step-by-step explanation:

1km= 1000m

1hr =60sec

Other Questions
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