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
Molodets [167]
3 years ago
15

the second term of a geometric sequence is 18 and the fourth term is 8 find the common ratio . And find the sum of the first 6 t

erms
Mathematics
1 answer:
777dan777 [17]3 years ago
8 0

Answer:

  • ratio: 2/3
  • sum: 73 8/9

Step-by-step explanation:

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

You have the 2nd and 4th terms, so ...

  a2 = a1·r^(2-1) = a1·r

  a4 = a1·r^(4-1) = a1·r^3

We can find r from the ratio ...

  a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9

Then r is ...

  r = √(4/9) = 2/3 . . . . the common ratio

The first term is ...

  a2 = 18 = a1·(2/3)

  a1 = (3/2)·18 = 27

__

The sum of the first 6 terms is ...

  Sn = a1·(r^n -1)/(r -1)

  S6 = 27·((2/3)^6 -1)/(2/3 -1)

  S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9

The sum of the first 6 terms is 73 8/9.

_____

<em>Check on the sum</em>

The first 6 terms are ...

  27, 18, 12, 8, 5 1/3, 3 5/9

Their sum is 73 8/9, as above.

You might be interested in
If the length of a side of an<br> equilateral triangle is x, what is half of the perimeter?
nataly862011 [7]

Answer:

3/2 x

Step-by-step explanation:

length of a side of an  equilateral triangle is x

The perimeter is

P = 3s  where s is the side length

P = 3x

1/2 of the perimeter

1/2 (3x)

3/2 x

4 0
3 years ago
-4x - 3 = -6x + 9 need help please.​
Valentin [98]

Answer:

6

Step-by-step explanation:

-4x -3 = -6x +9

-4x = -6x +12

2X = 12

x = 6

8 0
2 years ago
Read 2 more answers
Angle Q = 85° Determine angle O.
kkurt [141]

Answer:

∠O = 95°

Step-by-step explanation:

since ∠Q = 85°, arc NOP = 2(85°) = 170°

arc PQN = 360° - arc NOP

arc PQN = 360° - 170° = 190°

∠O = 1/2(arc PQN) = 1/2(190°) = 95°

4 0
2 years ago
What is the measure of n?
horsena [70]

The value of n is 32 if the total; base length is 12(8+4) and n is the length of the perpendicular.

<h3>What is a right-angle triangle?</h3>

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We can use the altitude rule:

8/n = n/4

n² = 32

n = √32

Thus, the value of n is 32 if the total; base length is 12(8+4) and n is the length of the perpendicular.

Learn more about the right angle triangle here:

brainly.com/question/3770177

#SPJ1

8 0
1 year ago
THIS IS FOR 60PTS A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to spend no more than $24 o
Nataly_w [17]

Answer:

$21/$1.50 per mile =14 miles. The units match $/($/mile), so division was the proper operation.

C

Step-by-step explanation:

Plz mark brainliest i need it

6 0
3 years ago
Read 2 more answers
Other questions:
  • Anybody know the answer?
    9·2 answers
  • Thomas has 132 crayons if he keeps 1 dozen in each box how many boxes of crayons does he have
    7·1 answer
  • What is the perimeter of trapezoid JKLM? j -7,4 k -4,4 m -8,3 l -2,3
    14·1 answer
  • One pound of grapes costs $2. at this rate how many dollars will c pounds of grapes cost
    11·1 answer
  • What is a curved mirror
    12·2 answers
  • How to solve this equation 6x^2-2x+5+2x^2-7x-11
    15·1 answer
  • Help plsss for brainliest
    5·1 answer
  • Bella is x years old. Jake is 9 years older than Bella. Five times Jake’s age is equal to 300. (a) Write an equation that could
    13·1 answer
  • What is 6x + 4x?<br> Explain your reasoning.
    5·1 answer
  • Find the missing side. Round to the nearest tenth.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!