Indicate a general rule for the nh term of this sequence.
12a, 15a, 18a, 21a, 24a,...

Answers

Answer 1

Answer:

The general rule for the nth term of this sequence will be:

[tex]a_n=3na+9a[/tex]

Step-by-step explanation:

Given the sequence

12a, 15a, 18a, 21a, 24a,...

An arithmetic sequence has a constant difference 'd' and is defined by  

[tex]a_n=a_1+\left(n-1\right)d[/tex]

Here,

a₁ = 12a

computing the differences of all the adjacent terms

d = 15a-12a = 3a, d = 18a-15a=3a, d=21a-18a=3a, d=24a-21a=3a

using the nth term formula

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substituting a₁ = 12a, d = 3a

[tex]a_n=12a+\left(n-1\right)3a[/tex]

     [tex]=12a+3na-3a[/tex]

     [tex]=3na+9a[/tex]

Therefore, the general rule for the nth term of this sequence will be:

[tex]a_n=3na+9a[/tex]


Related Questions

If F(x)= logx, which statement best describes the transformation (0.5(x-3)) + 12

Answers


Answer: Shifted up 10.5 units
Vertical compression
Explanation:
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

A bag contains 100 marbles. Some are blue, and the rest are white. There are 24 blue
marbles for every 1 white marble. How many blue marbles are in the bag?
Explain your reasoning.

Answers

Answer:

there would be 96 blue marbles and 4 white ones

Step-by-step explanation:

theres 100 marbles. every 24 marbles is 1 white marble. 24+1=25 25×4=100 24×4=96 1×4=4

Answer:

96 blue

Step-by-step explanation:

There are 24 blue for every 1 white so

24+1 = 25 blue marbles

25x4 = 100 or the total amount

100(total)-4 (white)

= 96 blue marbles

Seven pounds of grapes cost $10.43. How much would 4 pounds cost?​

Answers

Answer:

5.96

Step-by-step explanation:

Select the statement that indicates that the triangles in each pair are congruent. 50 points

Answers

Answer:

C) ΔEFG ≅ΔLMN

Step-by-step explanation:

C) ΔEFG ≅ΔLMN

A car is traveling at a rate of 41 miles per hour. At this rate, how many miles will the car will travel in 30 minutes? Pls it will make my christmas

Answers

Answer:

41/2=20.5

Step-by-step explanation:

The answer is 41/2 = 20.5

Can some one help me plz

Answers

Answer:

1b

1

Step-by-step explanation:

2. Sandra has earned 284 out of 300 points in Math class. What grade did Sandra
make in her math class? (Round your answer to the nearest whole percent)

Answers

Answer:

95%

Step-by-step explanation:

300/284 = 0.946666... rounded the the whole percent is 95%

300 * 95% = 285

The following shape is a rhombus. Find the measure of each unknown angle:

90
52
38
46
72

Answers

Answer:

63 42

53

53

52

Jdjdjdjfh

m∠APD = m∠DPC = m∠BPC = m∠APB = 90°m∠DPA = 38°m∠PAB = 52°m∠PCD = m∠PCB = 52°mABP = m∠CBP = 38°.

Properties of a rhombus:Diagonals of a rhombus intersect each other at 90°. Sum of two adjacent angles of a rhombus is 180°.Diagonals bisect opposite angles.

By using property - 1,

m∠APD = m∠DPC = m∠BPC = m∠APB = 90°

Apply triangle sum theorem in ΔAPD,

m∠DAP + m∠APD + m∠DPA = 180°

52° + 90°+ m∠DPA = 180°

m∠DPA = 38°

By using property - 3,

m∠PDC = m∠DPA = 38°

m∠PAB = 52°

By using property - 2,

m∠ADC + m∠DCB = 180°

2(38°) + m∠DCB = 180°

m∠DCB = 104°

Therefore, m∠PCD = m∠PCB = [tex]\frac{104}{2}[/tex] = 52°

m∠DAP = m∠BAP = 52°

Since, m∠ADC = m∠ABC = 76°

Therefore, mABP = m∠CBP = [tex]\frac{76}{2}=38^\circ[/tex]

         Hence, m∠APD = m∠DPC = m∠BPC = m∠APB = 90°, m∠DPA = 38°, m∠PAB = 52°, m∠PCD = m∠PCB = 52°, m∠BAP = 52°, mABP = m∠CBP = 38°.

Learn more about rhombus here,

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What's this? I don't know

Answers

Answer:

it's a quadratic formula

Step-by-step explanation:

in the formula, substitute the value of a as 1, b as 2 and c as -8

then, you will get ur answer

an open top box with a square base and a volume of 4m^3 is to be constructed what should the dimensions of the box be to minimize the surface area of the box?

Answers

Answer:

Dimensions of the box:

x =  1,26  ( the side of the square base )

h = 2,52   the heigh of the cube

Step-by-step explanation:

V(b)  = x² *h      x is the side of the square base, and h the heigh of the cube

The surface area of such cube is:

Area of the base   A(b)  = x²

Lateral area is  4*x*h

A(c) = x²  +  4*x*h

Now   x² * h  = v = 4 m³       ⇒  h = 4/x²   and

A(x)   =  x²   +  4/x

Tacking derivatives on both side of the equation:

A´(x)  =  2*x - 4/x²

A´(x) = 0       2*x  - 4/x²  =  0        ⇒   2*x³  -  4   = 0

x³  = 2

x  = 1,26 m

And  h = 4/(1,26)²        ⇒     h  =  2,52 m

How do we know the value of  x  =  1,26 is for a minimum value of A(x)

We find the second derivative of  A(x)

A´´(x)  =  2  -  (-4*2*x/x⁴)

A´´(x)  =  2  + 8/x³       is positive  A´´(x)  >  0

Then function A(x) has a minimum value at x = 1,26

The point (5,0) is a solution of 3 x - y > 4.
true or false ?

Answers

Answer:

false

Step-by-step explanation:

its not correct

The point (5,0) is NOT the solution; it’s false

Rank in Oder 4/9,2/3,7/12,5/6

Answers

Answer:

The sorted inputs in order from least to greatest is:

4/9 < 7/12 < 2/3 < 5/6

Step-by-step explanation:

Using the given inputs:

4/9,2/3,7/12,5/6

The least common denominator (LCD) is: 36

Rewriting as equivalent fractions with the LCD:

4/9,          2/3,          7/12,          5/6

16/36,       24/36,       21/36,       30/36

Sorting this table by the numerators of the equivalent fractions in order from least to greatest:

4/9            7/12             2/3             5/6

16/36  <    21/36    <     24/36  <     30/36

Therefore, the sorted inputs in order from least to greatest is:

4/9 < 7/12 < 2/3 < 5/6

An athlete's target heart rate, in beats per minute, is $80\%$ of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from 220. To the nearest whole number, what is the target heart rate of an athlete who is 26 years old

Answers

Answer:

155

Step-by-step explanation:

Since the question states that;

Maximum heart rate= 220 - athletes age

If athletes age = 26 years

Maximum heart rate= 220 - 26 = 194

Again;

athlete's target heart rate= 80% × Maximum heart rate

Athlete's target heart rate= 0.8 × 194= 155

I NEED HELP ASAP
Which equation represents the situation below?

Bry's account was overdrawn by $11.85, so he deposited $11.85 into his account.
A.
(-11.85) + (-11.85) = 0
B.
(-11.85) – 11.85 = 0
C.
11.85 – (-11.85) = 0
D.
(-11.85) + 11.85 = 0

Answers

Answer:

D

Step-by-step explanation:

overdrawn = =negative so -11.85+11.85 or option D

Hope this helps plz hit the crown ;D

Number of doctors and lawyers asked whether they prefer to watch medical dramas or court dramas on TV according to the table below the percent of a lawyer surveyed preferred medical dramas

Answers

Answer:

Although doctor-centric dramas can be entertaining, they're usually filled with a number of inaccurate portrayals of the medical field.

To see where which popular shows get the details right and which ones are loaded with problems, Insider consulted with real doctors and nurses.

Here's how the experts really feel about popular medical shows.

Note: The Entertainment Value and Medical Accuracy scores on each slide are the averages of the scores (out of 10) that the experts provided for each show.

Step-by-step explanation:

please mark me as brainlest answer hope this helps

Determine the largest integer value of x in the solution of the following inequality.
3x+9 < -13

Answers

Answer:

-7

Step-by-step explanation:

I need help bad I will mark you as king or what every pkz get it right I can’t get it right plz help

Answers

Answer:

d=6c it looks like. good luck

I need help with this!!​

Answers

Answer:

14 burgers

Step-by-step explanation:

3 1/2 ÷ 1/4 = 14

RIGHT TRIANGLES & TRIGONOMETRY MATH
TOMMOROW DUE PLZZZ

Answers

Answer:

sin d= 20/29

cos d= 21/29

tan d= 20/21

sin e= 21/29

cos e= 20/29

tan e= 21/20

7) x=47  (25tan(62))

8) x=25.1 (11/sin(26))

9) x=23.8 (32sin(48))

10) x=29.6 (29/cos(12))

11) x=21 degrees (invcos(14/15))

12) x=39.6 degrees (invtan(19/23))

13) x=58 degrees (invcos(9/17))

14) x=72.9 degrees (invsin43/45))

Step-by-step explanation:

good luck m8 it gets harder trust me

also srry if something is wrong im so exhausted thxbye

A student survey asked: "How tall are you (in inches)?" Here's the data:
67, 72, 73, 60, 65, 86, 72, 69, 74
Give the five-number summary.
A. 60, 67, 72, 73, 74

B.0, 60, 70. 89. 74, 100

C. Median 73 mean: 70.89, interquartile range (IQR): 5, min: 60, max: 74

D. 60, 66, 72. 73.5. 86​

Answers

Answer:

a

Step-by-step explanation:

Susan can solve 8 math problems in 20 minutes while Betsy can solve the same 8 math problems at a rate of 1 problem per 5 minutes. Who works faster? Show your work.

Answers

Susan works faster
if you solve 8 problems in 20 minutes, that is faster than 1 problem per minute because even once you do 5 problems you are at 25 minutes and that is longer than the 20 minutes

25 35 47
17 5 61
11 72 ??



Answers

Answer:

There is no pattern to it.

Step-by-step explanation:

An electrician charges a $100 flat fee, plus $75 per hour to work on a house.

Answers

Answer:

y=75x+100

Step-by-step explanation:

Given a point A(-3,-14, it is dilated by some scale
factor to A' (-9,-3). If the same dilation is applied
to B(-1,-5), what are the coordinates of B'?

Answers

The question was rewritten because it has an obvious mistype.

Answer:

The coordinates of B' are (-3,-15)

Step-by-step explanation:

We are given the point A(-3,-1) and we know it was dilated to the point A'(-9,-3) by some scale factor.

The scale factor can be found by dividing each coordinate of A' by the same coordinate of A. Let's call the factor as k:

k = -9/(-3) = 3

k = -3/(-1) = 3

Thus the scale factor is 3.

If we apply the same factor to B(-1,-5), we get the coordinates of B' as:

B'( 3*(-1) , 3*(-5) ) = B'(-3,-15)

The coordinates of B' are (-3,-15)

I dont understand this problem ​

Answers

Answer:

64 ; 8

Step-by-step explanation:

a² ± 2ab + b² = (a ± b)²

x² + 2(8)(x) + 8² =

x² + 16x + 64 =

(x + 8

A football team loses 7 yards on each of 2 consecutive plays. Find the total change in yards from where the team started.

Answers

Multiply the number of plays by the number of yards lost in a play. But to "get it" you need to also know how many yards were lost in a play, which was not stated in the problem.

HOPE THIS HELPS! !!!

A class has average height of 68 inches and a standard division of 2 inches what height do you need to be taller than 90% of the class please round your answer to the nearest thousandth.

Answers

Answer:

65.426

Step-by-step explanation:

Given that:

Mean height (m) = 68 inches

Standard deviation (s) = 2 inches

Height required to be taller than 90% of the class :

P(Z > x) = 0.9

The corresponding Zscore is - 1.282 (Z probability calculator)

Using the Zscore relation :

Zscore = (x - m) / s

-1.282 = (x - 68) / 2

-1.282 * 2 = x - 68

-2.564 = x - 68

-2.564 + 68 = x

x = 65.436

There are 15 applicants for four jobs : Computer Programmer , Software Tester , Manager , and Systems Engineer
IS THIS A PERMUTATION OR COMBINATION ?

Answers

Answer:

it Permutation 32760

Step-by-step explanation:

it permutation because the order is matter

15p4=32760

This is the case of a combination and the possibility of arrangement is 1365.

What is the combination?

The combination is the process of choosing items or things from a bigger group where the order is irrelevant. The combination formula aids in determining the number of possible combinations that can be created by selecting a portion of a bigger set of objects.

Given There are 15 applicants for four jobs: Computer Programmer, Software Tester, Manager, and Systems Engineer.

From the difference between permutation and combination:

A permutation is a method of arranging all the members in order. The combination is a selection of elements from a collection.

Since the order is not asked thus this is the case of a combination

and total arranging possibility = ⁿCₓ

total arranging possibility = ¹⁵C₄

total arranging possibility = 15! /( 11! * 41)

total arranging possibility = 1365

therefore, This is a combination case, and the number of possible arrangements is 1365.

Learn more about combination here:

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Please help me I don’t understand.

An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tiles has a length 1/2 inch and width 1/6 inch. The actual tiles have a length 1/3 ft and width 1/9 ft. What is the area of a tile in the model to the area of the actual tile?

Answers

Answer:

1 : 64

Step-by-step explanation:

Model:

1/2 in * 1/6 in = 1/12 in^2

Real:

1/3 ft * 1/9 ft = 1/3 * 12 in * 1/9 * 12 in = 16/3 in^2

model : real

1/12 / 16/3 = 1/12 * 3/16 = 3/192 = 1/64

model : real = 1 : 64

Please help. First correct answer I’ll mark as brainliest

Answers

Answer:

AA similarity, triangle CBA is congruent to triangle CST

Step-by-step explanation:

angle ACB and angle TCS are congruent by the vertical angles theorem

The picture marks that angle B and angle S is congruent

since 2 angles are congruent, the triangles are similar by the AA similarity

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