h(1)= 9

h(n)=h(n−1)⋅(-3)

Find an explicit formula for h(n).

h(n)= ?

Answers

Answer 1

Given:

[tex]h(1)=9[/tex]

[tex]h(n)=h(n-1)\cdot (-3)[/tex]

To find:

The explicit formula for h(n).

Solution:

We have,

[tex]h(n)=h(n-1)\cdot (-3)[/tex]         ...(i)

It is the recursive formula of a geometric sequence. It is of the form

[tex]a(n)=a(n-1)\cdot r[/tex]         ...(ii)

where r is the common ratio.

On comparing (i) and (ii), we get

[tex]r=-3[/tex]

We have, [tex]h(1)=9[/tex] so the first term of the geometric sequence is [tex]a=9[/tex].

The explicit formula for a geometric sequence is:

[tex]h(n)=ar^{n-1}[/tex]

Substitute a=9 and r=-3 to get the explicit formula for the given sequence.

[tex]h(n)=9(-3)^{n-1}[/tex]

Therefore, the required explicit formula is [tex]h(n)=9(-3)^{n-1}[/tex].


Related Questions

Which temperature is greater, -20F or -60F

Answers

Answer:

-20

Step-by-step explanation:

Answer:

It's -20F :)

Step-by-step explanation:

hsbshehehebvdhshhakakkanabsbxh

en una encuesta a 200niños sobre el programa de T.V. que más les gusta ver ,se encontró que a 30 niños ven dibujos animados 45 niños miran películas animadas solamente 55niños miran programas sobre animales 38 niños miran programas sobre animales y dibujos animados 32 niños miran los tres tipos de programas encuentra el porcentaje de cada grupo​

Answers

Answer:

15% de los niños solo ven dibujos animados, 22.5% solo ven películas animadas, 27.5% ven programas sobre animales, 19% miran programas sobre animales y dibujos animados, y 16% ve los tres tipos de programas.

Step-by-step explanation:

Dado que en una encuesta a 200 niños sobre el programa de TV que más les gusta ver se encontró que 30 niños ven dibujos animados, 45 niños miran películas animadas, 55 niños miran programas sobre animales, 38 niños miran programas sobre animales y dibujos animados y 32 niños miran los tres tipos de programas, para determinar el porcentaje de cada grupo​ se deben realizar los siguientes cálculos:

30/200 = 15/100 = 15%

45/200 = 22.5/100 = 22.5%

55/200 = 27.5/100 = 27.5%

38/200 = 19/100 = 19%

32/200 = 16/100 = 16%

Así, 15% de los niños solo ven dibujos animados, 22.5% solo ven películas animadas, 27.5% ven programas sobre animales, 19% miran programas sobre animales y dibujos animados, y 16% ve los tres tipos de programas.

What is the distance between (3,5) and (7,3)

Answers

Answer: (4, 2)

Explanation: 7 - 3 is 4 and 5 - 3 is 2

list the factors of 5i^2+12i−32 i need help fast

Answers

Answer:

Step-by-step explanation:

5i² + 12i - 32i  = 5i² - 20i

                      = 5i² - (5*4*i)

                      = 5i(i - 4)

can some help me pick the right answer for (9 + t) /12 = -3
45
-45
36
-36

Answers

Answer:

(9 + t)/12=-3

(9-45)/12

-36/12

= -3

answer = -45

Solve the following equation:
1/3(y - 2) -5/6 (y + 1) =3/ 4(0 - 3) - 2

Answers

Answer:

11/5

Step-by-step explanation:

If you need help with more problems like this you can use m a t h w a y. (remove the spaces)  :)

Someone help and plz make sure it’s right

Answers

Answer:

80 degree angle is the right answer

2 people working at the same rate will take 9 hours to paint a room.
a) Assuming that they all work at this rate, how long will it
take 3 people to paint the room?
hours
(2)
b) In fact, the third person works at a faster rate.
How does this affect the time to paint the room?
Will it be
A faster?
B slower?
or

Answers

Answer:

a)6 hrs

b)faster

Step-by-step explanation:

a) 9*2/3=6

Orlando wants to buy a new TV. The price was $985. When he goes to the store a second time, he found that price was marked down by 35%. What is the new price of the TV?​

Answers

The TV is now $640.25 after the mark down. First you have to find 35% of $985 which is 344.75 then subtract that from 985 and you get 640.25.

Erin is testing how a component used in a manufacturing process responds to rapid changes in temperature over a period of 30 seconds. During the test, the temperature of the component in degrees Fahrenheit at seconds is modeled by the quadratic function () -- +241 fort=0 tr = 30
Using this model, which statements are true about the test? Choose all that are correct
The initial temperature of the component is o"
The temperature is increasing for the duration of the experiment
The temperature of the component is never less than zero degrees
The component has the same temperature att and t 24
The maximum temperature reached by the component during the experiment is 144"

Answers

Answer:

The answer will be A and D and E

Step-by-step explanation:

Mei has 2 yellow teacups and 5 brown teacups Which ratio compares the number of brown teacups to the total number of teacups

Answers

Answer:  5: 7

Step-by-step explanation:

The total number for teacups: 2 yellow teacups + 5 brown teacups = 7 teacups

the ratio compares the number of brown teacups to the total number of teacups is :

5: 7

The ratio that compares the number of brown teacups to the total number of teacups is 5: 7

What is the ratio?

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that Mei has 2 yellow teacups and 5 brown teacups.

The total number for teacups is;

2 yellow teacups + 5 brown teacups = 7 teacups

Therefore, the ratio compares the number of brown teacups to the total number of teacups can be;

5: 7

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ2

please help this is due soon

Answers

the answer is 60degree..hope it helps u

HELP ANSWER GETS BRANLIEST ANSWER!

Answers

Answer: -5/4

Step-by-step explanation: You can use the graph to count the slope. The change in y is -5 and the change in x is 4, and slope is change in y over change in x.

Somebody help me ASAP noww

Answers

Answer:

65

Step-by-step explanation:

That is a 180 split so 180-115=65

Help help help help help help help

Answers

Answer:

35/14

Step-by-step explanation:

Volume = 4 * h * 7 / 2 = 14h

35/14 = h

Will give brainliest

Answers

Answer:

The third option

Step-by-step explanation:

-1 - 3 = -4

1 - 3 = -2

3 - 3 = 0

5 - 3 = 2

5 cm 7 cm 15 cm What is the surface area of the figure? by square centimeters ​

Answers

Is this a right triangle or triangle is solving for?

If x/5 = 4/15, what is the value of x? Please hurry and answer!!! In a test!!!!​

Answers

Answer:

x= [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

(✿◡‿◡) <-- she helped u on your test, the least you can do is give her brainliest

Which figures appear to be congruent?

An image of 5 triangles on a 14 by 12 grid is shown.Triangle 1 has a base that is 4 units long. The upper vertex is 4 units above the midpoint of the base. To the right, triangle 2 has a horizontal leg that is 3.5 units long and a vertical leg that is 4 units long. A small square is positioned in the triangle at the lower left vertex. Below triangle 1, triangle 3 has a horizontal leg that is 3.5 units long and a vertical leg that is 4 units long. A small square is positioned inside this triangle at the upper right vertex. Triangle 4 is toward the center of the grid. It has a horizontal leg that is 1 unit long and a vertical leg that is 4 units long. A small square is positioned inside this triangle at the upper right vertex. Triangle 5 is to the lower right. It has a horizontal leg that is 6 units long and a vertical leg that is 4 units long. A small square is positioned inside this triangle at the lower left vertex.
A. 1, 2, and 3
B. 1 and 4
C. 1 and 5
D. 2 and 3

Answers

Answer:

D

Step-by-step explanation:

which table and graph represents the equation y=2x i give brainly wjo ever it correct

Answers

Answer:

graph a and table a=B

Step-by-step explanation:

This is because for table a, if you subsite the numbers of x it would give you the answer for y such as y=2x, and since x is 2 y is 4, which is shown on the graph. And since it does not have any add ons, if you make x 0 it would be 0 so it would also be proportional through the orgin. so graph A is also correct.

3) In Carter's math class, 20\% of students earned an A on a test. If there were 30 student in the class, how many did not get an A.

Answers

Answer:

24 students did NOT get an A

Step-by-step explanation:

30x.20=6

30-6=24

Factor 35y+40z please help.

Answers

Answer:

i judt want points

Step-by-step explanation:

5(7y+8z) is the answer lmk if u want she’s

Plz help me Jen can jump rope 80 times in 60 seconds. If she jumps at a constant ratio of seconds to jumps, how many jumps can she make in 15 seconds?

Answers

Answer:

The answer is 4

Step-by-step explanation:

You just divide 80 by 15.

She can jump rope 20 times in 15 seconds

What is Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

What are Arithmetic operations?

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that Jen can jump rope 80 times in 60 seconds.

We have to determine the number of jumps can she make in 15 seconds.

Let the number of jumps would be x she can make in 15 seconds

Since she jumps at a constant ratio of seconds to jumps

So according to proportionality,

⇒ 80/60 = x/15

⇒ x = 15(80/60)

⇒ x = 20

Hence, she can jump rope 20 times in 15 seconds.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ2

I NEED HELP IM BEGGING WILL MARK BRAINLEST
JUST ANSWERS NO WORK NEEDED

Answers

Answer:

a = 5 c =11

Step-by-step explanation:

Answer:

sqrt[(80^2) + (20^2)] = (bottom base of the entire rectangle)

= 20(sqrt(17)) units or about 82.46211 units

find angle at bottom corner

arctan(20/80) = about 14.04624 degrees

cos(14.04624) = 20(sqrt17) / (80+a)

solve for a: --> a = 5 units

use pythag for side c

(20^2) + (5^2) = c^2

c is about 20.6155 units or 5(sqrt17)

Step-by-step example:

The population of a city is 250,000 and the annual growth rate is 2.2% Write an equation to model the population y after x years.

Answers

Answer:

bueno, es 3.70 así que espero que ayude um buena suerte ~ nena ~

Step-by-step explanation:

Which expressions are polynomials? Select each correct answer. x2−x√+2 2 + s 4x³ + y​

Answers

Answer:

Answers are

Y

2+s

4x^3+y

Step-by-step explanation:

Help pls show brainly

Answers

Answer:

10

Step-by-step explanation:

125 divided by 12.5

Answer: 10 dresses

Step-by-step explanation:

125/12.5=10

For every dress she needs 12 1/2 yards of fabric so what multiple of 12.5 is equal to or less than 125 and thats 10

Evaluate: 5*5/7
enter your answer as a proper fraction or mixed number

Answers

Answer:

3 4/7

Step-by-step explanation:

5 times 5/7 = 25/7

= 3 4/7

Answer:

3 4/7

Step-by-step explanation:

5/1 x 5/7 = 25/7 = 3 4/7


[tex]81 \frac{1}{2} \times 121 \frac{1}{2} [/tex]

Answers

81.5 x 121.5= 9,902.25

Can someone help me pls

Answers

The distance from the lighthouse to the boat will be given by: tan θ=opposite/adjacent θ=angle of depression=23 opposite= height of the lighthouse adjacent=distance from the boat to the bottom of the light house hence tan 23=210/a thus solving for a we obtain: a=210/tan23 hence a=494.73 ftHOPE IT HELPS !!!
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