1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Angelina_Jolie [31]
2 years ago
13

The sum of the second and third terms of G.P is six times the fourth term. Find the two possible values of the common ratio​

Mathematics
1 answer:
andrew-mc [135]2 years ago
8 0

Answer:

Step-by-step explanation:

Let “a” be the first term and ”r” the common ratio of the GP. Then,

f(n) = ar^(n - 1).

f(2) + f(3) = 6f(4). (given)

ar + ar^2 = 6ar^3, or

1 + r = 6r^2, or

6r^2 - r - 1 = 0,

(3r + 1)(2r - 1) = 0.

r = -1/3, or 1/2.

If the common ratio is positive and the second term is 8 we have,

ar = 8, or

a*1/2 = 8, or a = 16.

f(n) = 16*(1/2)^(n - 1) = 2^4*2^(1 - n), or

f(n) = 2^(5 - n).

The first six terms of the GP are : 16, 8, 4, 2, 1, 1/2,…

××××××××××

Checking : f(2) + f(3) = 6f(4), (given).

LHS = 8 + 4 = 12.

RHS = 6* 2 = 12.

LHS = RHS.

You might be interested in
HELP PLEASE!- the growth of a kitten is described by the equation y=2.5+4, where y represents the kitten's weight in ounces x we
erastovalidia [21]
4 is the X variable so it means it is 4 weeks after the kitten is born.
14 is the Y variable so it means it is 14 ounces after 4 (this is the X variable) weeks.
5 0
3 years ago
The mass of a grain of sand is about 103 gram.
KatRina [158]

1 grain = 103g

2kg = 2000g

grains = 2000g/103g = 19.417

Answer:

About 19.417 grains

3 0
3 years ago
Is 5 a solution to the equation 2x^2 + 10 = 60 yes or no
cricket20 [7]
2(5)^2+10
2(25)+10
50+10
60
Yes
8 0
3 years ago
Read 2 more answers
4. Solve x -- 7 = 25.<br> A 18<br> B 32
gregori [183]

Answer:

B

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
What is the domain of the function y=tan (x/8)<br> Please Help<br> 15 Points
7nadin3 [17]

1. You have the function y=tan(\frac{x}{8} )

2. You know that y=\frac{sinx}{cosx} with cosx\neq 0, because the division by zero is not defined. So , cosx=0 for \frac{(2n+1)\pi}{2} where n is a integer number.

3. Then, to find the domain of the function given in the problem, you must make \frac{x}{8} \neq \frac{k\pi}{2}  \\ x\neq 4k\pi

Where k is odd number.

4. Therefore:

x\neq 4\pi (2n+1)

5. Finally, the domain is: 4\pi (2n+1)

The answer is: 4\pi (2n+1)

5 0
3 years ago
Read 2 more answers
Other questions:
  • HELP ME ASAP!!!!!!!!!!!!!!! PLEASEEEEEEEEEEEEEEEEEEEEE
    13·2 answers
  • What is $0.1369 rounded to the nearest cent
    11·1 answer
  • A number minus one is at the most nine, or two times the number is at least twenty-four.
    13·1 answer
  • A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in
    14·1 answer
  • What is the median of the data set represented by the box plot 37, 45, 50, 67, 75
    13·2 answers
  • Classify the triangle.<br><br>obtuse<br><br>equiangular<br><br>right<br><br>acute
    12·2 answers
  • One of the zeros of f(x)=x^3-6x^2+11x-6 is 3. What are the other zeros of the function?
    7·1 answer
  • What is the slope for this? Please tell :)
    7·1 answer
  • NUMBER 2 AND 3. GIVING BRAINLIEST!!
    15·2 answers
  • Help me cause why not
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!