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
svp [43]
3 years ago
15

The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?

Mathematics
1 answer:
Lena [83]3 years ago
3 0

Answer:

possible values of 4th term is 80 & - 80

Step-by-step explanation:

The general term of a geometric series is given by

a(n)=ar^{n-1}

Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term

  • Given, 5th term is 40, we can write:

ar^{5-1}=40\\ar^4=40

  • Given, 7th term is 10, we can write:

ar^{7-1}=10\\ar^6=10

We can solve for a in the first equation as:

ar^4=40\\a=\frac{40}{r^4}

<em>Now we can plug this into a of the 2nd equation:</em>

<em>ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}</em>

<em />

<em>Let's solve for a:</em>

<em>a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640</em>

<em />

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

<u>Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:</u>

ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80

possible values of 4th term is 80 & - 80

You might be interested in
Factor completely 3bx^2 - 9x^3 - b + 3x​
Anna11 [10]

Factor out the common terms in the first two terms, then in the last two terms;

3x^2(b - 3x) - (b - 3x)

Factor out the common term b - 3x

<u>= (b - 3x)(3x^2 - 1)</u>

5 0
3 years ago
Find a point on the ellipsoid x2+y2+4z2=36x2+y2+4z2=36 where the tangent plane is perpendicular to the line with parametric equa
Anvisha [2.4K]

Answer:

A point on the ellipsoid is (-4,2,2) or (4,-2,-2)

Step-by-step explanation:

Given equation of ellipsoid f(x,y,z) :x^2+y^2+4z^2=36

Parametric equations:

x=-4t-1

y=2t+1

z=8t+3

Finding the gradient of function

\nabla f(x,y,z)=\\\nabla f(x,y,z)=

So, The directions vectors=(-4,2,8)

Now the line is perpendicular to plane when direction vector is parallel to the normal vector of line

\nablaf(x,y,z)=(2x,2y,8z)=\lambda(-4,2,8)

So, 2x=-4\lambda

\Rightarrow x=-2\lambda

2y=2\lambda\\\Rightarrow y=\lambda\\8z=8\lambda\\\Rightarrow z=\lambda

Substitute the value of x , y and z in the ellipsoid equation

(2\lambda)^2+(\lambda)^2+4(\lambda)^2=36\\9(\lambda)^2=36\\\lambda^2=4\\\lambda=\pm 2

With \lambda = 2

x=-2(2)=-4

y=2

z=2

With\lambda =- 2

x=-2(-2)=4

y=-2

z=-2

Hence a point on the ellipsoid is (-4,2,2) or (4,-2,-2)

7 0
3 years ago
What is the measure of angle C?
attashe74 [19]

Answer:

113

Step-by-step explanation:

supplementray means 180-67=113

5 0
2 years ago
Read 2 more answers
Given that g(x) = 2x ^ 2 - 2x + 8 , find each of the following. a) g(0) b) g(- 2) C) g(3) d) g(- x) e) g(1 - t)
raketka [301]

Answer:

g(-2)=20

Step-by-step explanation:

Given g(x)=2x^2-2x+8, substitute what is in the parentheses for x to find an output.

For g(-2), the term -2 is in the parentheses. Thus, substitute x=-2 into 2x^2-2x+8 to find g(-2):

g(-2)=2(-2)^2-2(-2)+8,\\g(-2)=2\cdot 4+4+8,\\g(-2)=8+4+8,\\g(-2)=\boxed{20}

5 0
2 years ago
Read 2 more answers
A rectangular plot measures 20 ft. By 30ft. A 3ft wide side walk surrounds it. Find the area of the side walk
r-ruslan [8.4K]

Answer:

336 feet²

Step-by-step explanation:

If we have a rectangle that is 30 by 20 feet, that means the area of that rectangle would be 20 × 30 feet squared, which is 600 ft².

If there is a 3 feet sidewalk surrounding it, that means that the end of the sidewalk will extend 3 feet extra around each side of plot. Since there are two ends to one side, that means an extra six feet is added on to each dimension. Therefore, 36 × 26 are the dimensions of the sidewalk+plot. 36 × 26 = 936 ft².

To find the area of the sidewalk itself, we subtract 600 ft² from 936 ft². This gets us with 336 ft².

Hope this helped!

3 0
2 years ago
Other questions:
  • 10 out of every 65 students order pizza for lunch. There are 416 students at her school. How many students will eat pizza at her
    6·1 answer
  • WILL GIVE BRAINLIEST
    6·2 answers
  • What are the different types of science
    6·2 answers
  • Which graph does not represent a function of x?
    10·1 answer
  • 18x + 9y use the distributive property to write an equivalent expression
    5·1 answer
  • Find an ordered pair ( x,y ) that is a solution to the equation.<br><br><br> 6x-y=1
    14·1 answer
  • How do you find the Interquartile of a box and whiskers plot?
    13·1 answer
  • Based on this scatterplot, if Carley runs in a 4-kilometer race and she maintains the same pace, how many minutes will it take h
    12·2 answers
  • Write the equation of a line in slope-intercept form that goes through:<br> (4,-1) and (-2,-4)
    10·1 answer
  • Factorise the expression 8ab + 7ac
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!