Given the first three terms of Geometric Sequence: 2b+2, b+4, b, where each of the tem is
positive, find
1) the value of b. (8)
ii) the first term and common ratio. (18,2/3)
(2009)​

Answers

Answer 1

Answer:

1. b = 8

2. First term (T₁) = 18

Common ratio (r) = 2/3

Step-by-step explanation:

1. Determination of the value of b.

2b+2, b+4, b

First term (T₁) = 2b + 2

2nd term (T₂) = b + 4

3rd term (T₃) = b

The value of b can be obtained as follow:

Common ratio = T₂/T₁ = T₃/T₂

T₂/T₁ = T₃/T₂

(b + 4)/(2b + 2) = b/(b + 4)

Cross multiply

(b + 4)(b + 4) = b(2b + 2)

Expand

b(b + 4) + 4(b + 4) = b(2b + 2)

b² + 4b + 4b + 16 = 2b² + 2b

b² + 8b + 16 = 2b² + 2b

Rearrange

2b² – b² + 2b – 8b – 16 = 0

b² – 6b – 16 = 0

Solving by factorisation

b² – 8b + 2b – 16 = 0

b(b – 8) + 2(b – 8) = 0

(b – 8)(b + 2) = 0

b – 8 = 0 or b + 2 = 0

b = 8 or b = –2

Since each of the terms are positive, therefore, b is 8.

2. Determination of the first term and common ratio.

2b+2, b+4, b

First term (T₁) = 2b + 2

b = 8

First term (T₁) = 2(8) + 2

First term (T₁) = 16 + 2

First term (T₁) = 18

2nd term (T₂) = b + 4

b = 8

2nd term (T₂) = 8 + 4

2nd term (T₂) = 12

Common ratio (r) = T₂/T₁

First term (T₁) = 18

2nd term (T₂) = 12

Common ratio (r) = 12/18

Common ratio (r) = 2/3


Related Questions

Trinh is catering a wedding that 112 people will attend. She is making two cakes, a chocolate cake and a carrot cake. 0.625 of the guests will be served chocolate cake and the rest will receive carrot cake. How many guests will get carrot cake?

Answers

O.625 * 112 = 70 people being served chocolate cake
112 - 70 = 42 guests that will get carrot cake

I hope this helps :)

Answer:

Step-by-step explanation:

70

A clothing retailer is gathering data on the amount of time each customer spends shopping in its stores. Each location collected 20 pieces of data and will compile that data to determine a population mean. One location has a sample mean of 32.5.

Which statement must be true about this situation?

A.
The population mean is also 32.5.
B.
There is not enough information to make a conclusion about the population mean.
C.
The population mean must be greater than 32.5.
D.
The population mean must be less than 32.5.

Answers

Answer:

B

Step-by-step explanation:

Please read the question and answer if you can 6th grade

Answers

Answer:

112 in

Step-by-step explanation:

14 x 8 = 112

The shaded region is half of the rectangle and also a triangle

Use formula: (L * W)/2
L = 14, W = 8
14 * 8 = 112/2 = 56
Solution: 56 in^2

Proving triangles similar

Answers

Answer:

x=11

Step-by-step explanation:

You do 38/3x+3 and 19/x+7 and then cross mulitply and get 57x+57=38x+266. Then yoy subtract 57 from 266 and get 57x=38x+209. Now you have to subtract 38 from 57 and then answer will be 19. So now you have 19x=209. Finally you divide 209 by 19 and get x=11. Good luck!

plsssssssssssssssss help​

Answers

Answer:

x = 7

Step-by-step explanation:

Find the point on the graph that has the y-value of 8. Determine its x-value.

please help mark brainliest ( no attachments please)

Answers

Answer:

I think 3 hours

Answer:

2/6 in 2 hours

Step-by-step explanation:

Two of the angles in a triangle measure 90 degrees and 7 degrees what is the measure of the third angle

Answers

The third angle should be 83.
90+7+83=180

Answer:

The third angle would be 83 degrees.

Step-by-step explanation:

Seeing that every triangle's angles will always add up to 180 degrees, we would do the following:

180-90=90

90-7=83 degrees.

Describe the relationship between the inputs and outputs in the diagram. Then complete the diagram. WILL NAME BRAINLIST!!!!!!!!!!!

Answers

Answer/Step-by-step explanation:

As the input increases by 1, the output decreases by 4. The missing number for the Input is 6, and the missing number for output is -17.

question is in picture please help!

Answers

Answer:

I’m not 100% sure but I think 120°.

Step-by-step explanation:

This is because, angles on a straight line add up to 180°. Because there is 60 degrees on one side of line B, this means the other section is 120° (120°+60°=180°) The angle labelled (3x) is alternate to the angle of 120°. Alternate angles are always equal, meaning that 3x is equal to 120°.

I hope this is right.

8. Change the fraction 3/4 to a percent.
A. 133%
B. 75%
C.63%
D. 34%

Answers

Answer:

B. 75%

Step-by-step explanation:

multiply the numerator and the denominator by 25. 3*25/4*25=75/100. 3/4=75%.

Answer:

75%

Step-by-step explanation:

Start by converting the fraction 3/4 into decimal

Divide the numerator by the denominator: 3 ÷ 4 = 0.75

Multiply the decimal by 100 and write the result with the percentage sign at the end 0.75 × 100 = 75%.

your awnser is, 3/4 = 75%

(sorry if this doesnt

make sence)

Please help me i need this turned in by tonight and i really don’t understand it but i don’t need an explanation i just need the awnser.

Answers

Answer: 180

Hope it helps

Step by step explanation:

1000*.18=180

a pack of candy bars has 6 bars. Each bar weighs 3.86 ounces. How much does the pack weigh?

Answers

Answer:

23.16 punces

Step-by-step explanation:

6x3.86=23.16

Answer: 23.16 ounces

Step-by-step explanation:

If there are 6 candy bars that each weigh 3.86 ounces, you need to add up all of the weights to find the total pack weight. 6*3.86=23.16

*If by any chance you need your answer to be in pounds, divide the answer by 16 (16 ounces in a pound). 23.16/16= 1.45 pounds

help plzzzz!!!!!!!!!​

Answers

Answer:

28.27

Step-by-step explanation:

3.14 x 9

is how to do this problem

Select the quadrant or axis where each ordered pair is located on a coordinate plane.

Answers

Answer:

(-5,7) 2nd          (8.5,-4) 4th       (0,5) y-axis

Step-by-step explanation:

5. chris is a school teacher who earns $32,000 for the 10-month school year. however, the salary is paid out in 12 monthly installments. how much does is the monthly paycheck? _________​

Answers

Answer:

$2666.66

Step-by-step explanation:

Yearly income = $32000

Each installment is 1/12 of a yearly income:

$32000/12 = $2666.66

Annual salary=32000

Monthly salary

32000/1216000/68000/3$2666.67

5a. Solve the equation. 4x = 32

Answers

Answer:

x=8

Step-by-step explanation:

have a good day

Answer:

x=8

Step-by-step explanation:

divide both sides of the by equation by 4

4x÷4=32÷4

x=32÷4

x=8

HELP PLEASE ASAP!!!!! 20 POINTS!!!!

Answers

I think it would be 10x+y because the slope is the amount he spends each month for the streaming service so then it would be 10x because x represent the number of months and then it’s +y because that’s the amount he already spent on the tablet

Please help ASP!!!! A= positive, B=Negative, C=Zero​

Answers

Answer:

B. Negative

Step-by-step explanation:

So first, we want to locate the variable.

y (x/y) = (y/1) (x/y)

           = (xy/y)

           = x

The y/y cancels out and now we know we need to find the sign of x. Because x is to the left of 0, it's negative. Anything to the left decreases and anything to the left of 0 is (-).

Factor 16a + 10.
(Please help)

Answers

Answer:

2(8a+5)

Step-by-step explanation:

To factor means to find a number that can divide all the terms in the expression and leave whole number quotients. The factor is written outside the bracket while the quotients are written inside the bracket. In the question, 2 can divide both 16a and 10 giving 8a and 5. This is how the answer was obtained.

16a+10
= 2(8a+5)
hope it helps

Can someone please answer these two questions

Answers

Answer:

A.

Step-by-step explanation:

What is the value of 7, 488 / 416

Answers

Answer:

8.17307692308

Step-by-step explanation:

7,488 divided by 416 is 18 (:

What is the median for the following set of data?

5, 7, 9, 11, 13, 13

A. 10
B. 8
C. 9
D. 11

Answers

C. 9
There are 6 numbers and half of 6 is 3 so the third one is 9!!

Answer:

Answer is 9

Step-by-step explanation:

I did the quiz also used a median calculator I don't think this will help but hopefully it dose or something

What’s another word for average

Answers

Answer:

Normal/standard

Step-by-step explanation:

Answer:

Ordinary

Step-by-step explanation:

A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a prime number a. 0.45 c. 0.71 b. 0.55 d. 0.73 Please select the best answer from the choices provided A B C D

Answers

Answer: B

Step-by-step explanation:

The prime numbers here are outcomes 2, 3, and 5.

Therefore, we must add the frequency numbers for these prime numbers:  

                36 + 44 + 30 = 110

Out of 200 dice rolls, 110 were prime numbers. This can be represented as:

              110/200 = 11/20 (fraction form)

                             = 0.55 (decimal form)

Therefore, the answer is b. 0.55

on the first one shows you how to solve it then second one is the problem just tell me the answer pls have a good day bye

Answers

Answer:

[tex] \frac{1}{2} + \frac{10}{12} \: = \: \boxed{\frac{4}{3}} [/tex]

Explanation:

[tex] \frac{1}{2} + \frac{10}{12} \: = \: \frac{1 × 6}{2 × 6} + \frac{10}{12} \: = \: \frac{6}{12} + \frac{10}{12} \: = \: \frac{6 + 10}{12} \: = \frac{16}{12} \: = \: \frac{16 ÷ 4}{12 ÷ 4} \: = \: \frac{4}{3}[/tex]

[Multiply the numerator and denominator by the common denominator so that both denominators are the same]

[Add the numerators together]

[Reduce the fractions and simplify by a common denominator until the denominator or numerator cannot be divided evenly]

VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.

Answers

Answer:

(2, 5)

Step-by-step explanation:

(x,y) -> )- y,x)

What is sin ?
What is a cos?

Answers

Answer:

Cos: adjacent / hypotenuse

In a right angled triangle, the cosine of an angle is: The length of the adjacent side divided by the length of the hypotenuse. The abbreviation is cos. cos(θ) = adjacent / hypotenuse. Well Done!

Sin: In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle.

hope this helps out, if not, i'm sorry

Step-by-step explanation:

Answer:

Sin=O/H

Cos=A/H

Step-by-step explanation:

Sin in full is some, a trigonometric ratio calculated by dividing the opposite over the hypotenuse.

Cos is in full cosine , also a trigonometric ratio calculated by dividing the adjacent over the hypotenuse.

Help please question in the picture

Answers

The correct answer is A.

The area of the square with a side length of 19 meters is 361 square meters.

To determine the area of a square, you multiply the length of one side by itself.

In this case, the side length is given as 19 meters.

To calculate the area of a square, you can use the formula:

Area = side length × side length

Area = 19 meters × 19 meters

Area = 361 square meters

So, the area of the square with a side length of 19 meters is 361 square meters.

For such more questions on area

https://brainly.com/question/25292087

#SPJ8

To find the area of a trapezoid, use the expression ½h(b¹ + b²), where h represents the height, b, represents the length of the top base, and by represents the length of the bottom base. What is the area of the trapezoidal table?​

Answers

is there supposed to be an image?? (comments, ill give answer if not, im

just confused)

Just want to confirm the answer is 4 more student because from 6 to 10 is 4
More or I’m wrong ?? Just please help me with yes or no thanks

Answers

Yes the answer is correct it’s 4

Answer:

Yes

Step-by-step explanation:

Your answer is correct ^^

Other Questions
Which incident gave President Johnson the opportunity to increase Americanengagement in Vietnam?1. The Soviets secretly placed dozens of nuclear missiles there2. The North Vietnamese attacked American ships in the Gulf of Tonkin3. China invaded South Vietnam with North Vietnamese forces4. The Viet Cong appealed to the United States to support their cause CO2 is made up of what two atoms and what is its common name? Which would be worse a change in DNA or a change in mRNA & why How do I submit a case study questions Answer if you knowDO NOT ANSWER IF YOU DO NOT KNOW THE ANSWERS*NO LINKS*Thank you :) Consider the United States' and the Soviet Union's plans for post-World War II Germany. How did they contrast? What questions do they ask on the flvs Spanish module 4 dba Solve for x. Assume that lines which appear tangent are tangent. What is (-m)n if m = 2 and n = -24? What is2 to the power of -1multiplied by 1multiplied by 3 to the power of 4 The leader of the British forces in the European Theater of war was ???? Douglas MacArthur Erwin Rommel Charles de Gaulle Bernard Montgomery My central claim is the recycling and pollution argument. What is the strong argument from both arguments? (PLEASE FAST) For the function given, state the starting point for a sample period: (t) = 100sin (50t 20). plz help Please help, will mark ya if right Which of the following is a sequence?A 3, 6, 9, 18, ...B 3, 6, 12, 18, ..C 0.3, 0.7, 1.3, 1.5, ...D 0.3, 0.6, 1.2, 2.4, Plss answer this will give brainliest 5 stars and a thxIVE BEEN ASKING FOR 2 DAYS :( OVERDUE Which kingdom contains the first eukaryotes? Mrs. Pham has 8 apples. She wants to give 3/4 of theapples to her students. How many apples will herstudents get? PLZ HELP ASAP Maria pushes a ball, and the ball rolls across the table. She wants to make the ball roll faster. Maria needs to push the ball A. with more strength. B. on a different table. C. on the other side of the table. D. with less strength. The graph shows two runners participating in a race.Which best describes the runners?Daniela had a 5-meter head start, and Leonard caught up to her at 25 meters. Daniela ran faster than Leonard through the entire race. Daniela gave Leonard a 5-meter head start and caught up to him at 25 meters. Daniela ran slower than Leonard, but she went faster at the end.