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
Luba_88 [7]
2 years ago
7

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

Mathematics
2 answers:
Step2247 [10]2 years ago
5 0
Hello,

a(2)=-6
a(3)=-6*r
a(4)=-6*r²
a(5)=-6*r^3=162
a(5)/a(2)=r^3=162/(-6)=-27==>r=-3

a(1)=-6/(-3)=2
a(2)=2*(-3)
a(3)=2*(-3)²
a(4)=2*(-3)^3
a(5)=2*(-3)^4

a(n)=2*(-3)^(n-1)




Answer
wlad13 [49]2 years ago
4 0

Answer:

an = 2 • (-3)^n - 1

Step-by-step explanation:

I have taken the test and this is the correct option :)

You might be interested in
How many solutions 2x+3y=-3 and 3x + 5y = -9
Sunny_sXe [5.5K]
Since the slopes of the two lines are the not equal, they will have only one solution. The solution will be a point and can be found using the method given below.

We can find the solutions by simultaneously solving the two equations.

From first equation, the value of y comes out to be:

2x+3y=-3 \\  \\ 
3y=-3-2x \\  \\ 
y= \frac{-3-2x}{3}

Using this value of y in second equation, we get:

3x+5( \frac{-3-2x}{3} )=-9 \\  \\ 
9x-15-10x=-27 \\  \\ 
-x=-27+15 \\  \\ 
-x=-12 \\  \\ 
x=12

Using this value of x, we can find y:

y= \frac{-3-2x}{3}= \frac{-3-24}{3} =-9

Therefore, there is only one solution to the given equations is which is (12, -9)
8 0
2 years ago
An airplane leaves an airport at 9:00 p.M. With a heading of 270 and a speed of 610 mph. At 10:00 p.M. The pilot changes the he
timama [110]

Answer:

2330.51 miles

Step-by-step explanation:

Given that the speed of the airplane = 610 mph.

The airplane leaves an airport at 9:00 P.M. with a heading of 270 degrees and at 10:00 P.M., the pilot changes the heading to 310 degrees.

So, for 1 hour the plane is heading at 270 degrees and for 3 hours, from 10:00 p.m to 1:00 a.m, the plane is heading at 310 degrees as shown in the figure.

As, distance = time x speed, so

The distance covered at 270 degrees, d_1 = 1\times610=610 miles.

The distance covered at 310 degrees, d_2 = 3\times610=1830 miles.

Total distance covered, d, is the magnitude of the sum of vectors \vec{d_1} and \vec{d_2} as shown in the figure.

The angle between the vectors \vec{d_1} and \vec{d_2}, \theta=310-270=40 degree.

Magnitude of sum of the vectors \vec{d_1} and \vec{d_2},

d= \sqrt{|\vec{d_1}|^2+|\vec{d_2}|^2+2|\vec{d_1}|\;|\vec{d_2}|\cos\theta} \\\\\Rightarrow d=\sqrt{610^2+1830^2+2|\vec{d_1}|\;|\vec{d_2}|\cos\(40^{\circ})}

\Rightarrow d=2330.51 miles

Hence, at 1:00 a.m, the airplane is at a distance of 2330.51 miles from the airport.

4 0
2 years ago
The upper quartile for the data set given below is. 14, 8, 23, 9, 11, 27, 22, 3, 17, 12, 29
LekaFEV [45]
Ok, first we need to organize.
<span>14, 8, 23, 9, 11, 27, 22, 3, 17, 12, 29
</span>3, 8, 9, 11, 12, 14, 17, 22, 23, 27, 29.

First, we need to find the median, the or the middle, which is 14.
Now that we know the median is fourteen, we take away all numbers to the left of 14, including 14: 17, 22, 23, 27, 29. Now just find the median in this new set of numbers. This will give us our upper quartile, which is 23. Hope this helped, and don't forget to drop a like.
5 0
3 years ago
Trigonometry question
Olegator [25]

Answer:

acute

Step-by-step explanation:

1. It cannot be right angle as the sides does not satisfy pythagoras theorem.

2. It cannot be obtuse angle as it does not satisfy the rule:

- the length of one side of a triangle must be greater than the differnce and less than the sum of the lengths of the other two sides.

4-3 =1 <6                     4+3=7>6  

8 0
2 years ago
To determine customer satisfaction with their service department, an automobile dealer randomly selects 20 hybrid-vehicle owners
Brrunno [24]

Answer:

The answer is stratified.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Other questions:
  • Factor 105^2-8^2 into two prime factors
    10·1 answer
  • What is 1 plus -1/8????????
    5·2 answers
  • If a car with an average speed of 50 miles per hour drives for 90 minutes, how far will it have gone?
    13·2 answers
  • An account earns simple interest.
    6·1 answer
  • The amplitude of y = -2 sin 3x is
    10·1 answer
  • How many vertices has a triangular pyramid and a triangular prism<br>​
    12·1 answer
  • The area of a square photo frame is 100 cm^2 find the length of the photo frame
    15·2 answers
  • "three food trucks are set up at points a, b, and c. each of the three trucks is the same distance from the food distributor. at
    14·1 answer
  • HELPPPPPPPPPPP PLSSSS FASTTTTTTT ASAPPPPPP WILL GIVE BRAINLIST
    12·1 answer
  • Help me with this question of O math​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!