Write the nth term of the following sequence in terms of the first term of the sequence.

2, -4, 8, -16, . . .

Answers

Answer 1

Answer:

        [tex]\bold{a_n=2\cdot(-2)^{n-1}}\\\\or\\\\\bold{a_n=(-1)^{n-1}\cdot2^{n}}[/tex]

Step-by-step explanation:

-4÷2 = -2

8÷(-4) = -2

-16÷8 = -2

So this is a geometric sequence with the first term of 2 and a common ratio of -2

the nth term of a geometric sequence:  [tex]a_n=a_1\cdot r^{n-1}[/tex]

Therefore:

            [tex]a_n=2\cdot(-2)^{n-1}\\\\a_n=2\cdot(-1\cdot2)^{n-1}=2\cdot(-1)^{n-1}\cdot2^{n-1}=(-1)^{n-1}\cdot2^{n-1+1}\\\\a_n=(-1)^{n-1}\cdot2^{n}[/tex]

Answer 2

Answer:

2(-2)^n-1

Step-by-step explanation:

Correct on Odyssey assignment. Hope this helps.


Related Questions

The circumference of a circle is double the perimeter of square having area 484 meter square . what is the area of the circle.​

Answers

Answer:

وتؤوثتيمسوثاسز لا لا لا وا

Answer:

616 sq. m

Step-by-step explanation:

The area of a square = 484

(Side)2 = 484  

side of a square = 22 m

According to the question,

circumference of a circle = perimeter of a square

2∏r = 4 × 22

r = 88 × 7/22 × 1/2  

r = 14 m

Area of a circle = ∏r2 = 22/7 × 142 = 616 sq. m

6. The swing set on the playgrounds is getting wobbly, and you have been asked to put outrigger boards to help stabilize it. If the crossbar of the swing is 10 feet off of the ground, the outrigger to be attached at a 40 degree angle, and you want to bury the outrigger boards 3 feet onto the ground, how long would the boards have to be? (Hint: the outrigger is the hypotenuse of a right triangle)

Answers

Answer:

[tex]X=18.6ft[/tex]

Step-by-step explanation:

From the question we are told that:

Height of swing's crossbar [tex]H=10ft[/tex]

Angle [tex]\theta=40 \textdegree[/tex]

Depth of outrigger [tex]d_=3ft[/tex]

Generally the equation for slant height l is mathematically given by

[tex]l=\frac{opposite}{sin\theta}[/tex]

Therefore

[tex]l=\frac{H}{sin\theta}[/tex]

[tex]l=\frac{10}{sin 40\textdegree}[/tex]

[tex]l=15.6ft[/tex]

Since the Depth of outrigger

[tex]d_=3ft[/tex]

Therefore Length of the board X

[tex]X=l+d[/tex]

[tex]X=15.6+3[/tex]

[tex]X=18.6ft[/tex]

HELP ASAP
What is the solution to the given system of equations?

y=4x-28

y=1.5x-18


1(-12,4)

2.(2,-12)

3.(7,0)

4.(7.5,2)

Answers

Answer:

Solution (4, -12)

None of the listed choices are a solution

Step-by-step explanation:

y = 4x - 28

y = 1.5x - 18

Set the equations equal since both equal y

4x - 28 = 1.5x - 18

Subtract 1.5x from both sides

2.5x - 28 = -18

Add 28 to both sides

2.5x = 10

Divide both sides by 2.5

x = 4

---------------------

use x= 4 in either equation

y = 4x - 28

y = 4(4) - 28

y = 16 - 28

y = -12

--------------------

Solution (4, -12)

I Need help with this question

Answers

Answer:

600

Step-by-step explanation:

Answer:

80 sq ft

Step-by-step explanation:

this is a trapezoid and the formula for area is:

1/2 x height x (sum of the bases, which are parallel)

A = 1/2(10)(10+6)

= 5(16)

= 80 sq ft

4. One week Lin's balance at the start of the week was (- $16) but she
earned $20 from babysitting and deposited it into her bank account. What was her
account balance at the end of the week?

Answers

her balance was $4 at the end of the week

Someone please please help me
No links or files

Answers

The answer is C for the first question. Blank 1 the answer is 29. Blank 2 the answer is 7. I hope this helps, have a good day!

2 3/8 • 1 1/6
Help step sis I'm stuck

Answers

Answer:

2.77083333333

Step-by-step explanation:

I assume. Do not hold me account for mistakes, I apologize if my work is incorrect. Have a good day/night :}

The person above me answer this

Plss help!!!!! Ty!

What is the area of this semicircle?

Answers

Area of a circle is pi (r)^2
So area of semi circle is 1/2 pi (r)^2
Then area =32 pi or ~100.53

Answer:

[tex]{\small{\boxed{\sf{\red{here's \: your \: solution...}}}}} \\ \\{\small{\boxed{\sf{\purple{area \: of \: semicircle \: =\pi \: r {}^{2} { \div 2} {} }}}}} \\ \\ \\{\small{\boxed{\sf{\purple{radius = 8cm }}}}} \\ \\ \\{\small{\boxed{\sf{\purple{area \: of \: semicircle \: =(22/7 \times 64) \div 2}}}}} \\ \\ \\{\small{\boxed{\sf{\purple{area \: of \: semicircle \: =100.57 \: cm {}^{2} }}}}}[/tex]

[tex]\small\mathfrak\green{Hope \: it \: helps \: \: .......| }[/tex]

True or false the median is always a number that is part of the data set?

Answers

Answer: Mostly. The middle number of the data is the median (set should be in order). If there are more than one middle numbers, then they are not the median but the average of those numbers are the median.

This is not necassary that average is always present in the listed information.

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

With a data set there are multiple number and always a middle whether or not its 2 numbers or 15. theres always a median.  


The ratio of the weights of A and B is equal to the ratio of the weights
of C and D. If A is 20 kg, B is 24kg and C is 40 find out the value of D .​

Answers

Answer:

D = 48kg

Step-by-step explanation:

The ratio of the weights of A and B is equal to the ratio of the weights

of C and D.

From the above question

A : B = C : D

This can also be interpreted as

A/B = C/D

A is 20 kg

B is 24kg

C is 40kg

D is ?

Therefore:

20/24 = 40/D

Cross Multiply

20D = 24 × 40

D = 24 × 40/20

D = 48

Therefore, D = 48kg

(no links or files) Solve this equation using the quadratic formula.

Answers

Answer:

x = 1/2,-3

Step-by-step explanation:

I think the answer is x = 1/2, -3.

Classify a triangle whose side lengths are 8, 16, and 18

A. Right Triangle

B. Acute Triangle

C. Obtuse Triangle

D. Isosceles Triangle

Answers

Answer:

Obtuse triangle

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as right angled, acute, obtuse and isosceles triangle.

In right angle triangle, one angle is 90°. The square of the longest side (hypotenuse) is equal to the sum of the square of the two sides.

An acute triangle is a triangle with acute angles (less than 90°). The square of the longest side is less than the sum of the square of the two sides.

An obtuse triangle is a triangle with one obtuse angle (greater than 90°) and two acute angles (less than 90°). The square of the longest side is larger than the sum of the square of the two sides.

An isosceles triangle is a triangle with two equal sides.

Given a triangle whose side lengths are 8, 16, and 18, the longest side is 18.

Since no two sides are the same hence it is not an isosceles triangle.

Also, 18² > 16² + 8²; therefore this is an obtuse triangle

Henrietta did an experiment. She started out with 800 bacteria cells. She found that the growth rate of the bacteria cells was 3.2%. Sketch the graph that represents the situation. Label the y-intercept and the point that represents the projected bacteria population 35 h from the time Henrietta started the experiment. I need help asap please

Answers

Answer:

See below

Step-by-step explanation:

Given

Initial number of bacteria = 800Growth rate = 3.2% = 1.032 times

Required equation:

B(t) = 800(1.032)^t, where B- number of bacteria, t- time in hours

The y-intercept is:

B(0) = 800*1.032^0 = 800The point (0, 800)

Bacteria population 35 in hours:

B(35) = 800*1.032^35 = 2409The point (35, 2409)

Evaluate the expression

Answers

22 I think I’m so sorryrrrr

Answer:

9+6(2)2+4

15(4)+4

60+4

64

Plz help meeee

y varies directly with x. If y = 15 when x = -18, find y when x = 1.6.

Answers

Answer:

-1.2

Step-by-step explanation:

I took the same direct variation test and got this one right

hope this helps!

Kylie spent $13.80 to buy 30 popsicles for her classmates. How much did each popsicle
cost?

Answers

Answer:

0.46

Step-by-step explanation:

13.80/0.46

just divide

if you divide 30 by 13.80 you should get $2.17

factorize 2x⁴+x³-14x²-19x-6
no spam and kindly explain your answer!​

Answers

Answer:

(x + 1)(x + 2)(2x + 1)(x - 3).

Step-by-step explanation:

From the leading and last coefficients, 2 and -6  the values +/- 1, +/-2 , +/- 3 could be roots of this equation ( well, up to 4 of them).

Try x = 1:

f(1) = 2(1)^4 + 1^3 - 14(1)^2 - 19(1) - 6 = -36 so its not 1.

f(-1) = 2 - 1 - 14 + 19 - 6 = 0 do x = -1 is a root.

Therefore (x + 1) is a factor  (By the factor theorem)

Try x = 2:

f(2) =  32 + 8 -56 - 38 - 6 = -6o so x =2 not a root.

f(-2) = 32 - 8 - 56 + 38 - 6 = 0 so x = -2 is a root and (x + 2) is a factor.

(x + 1)(x + 2) = x^2 + 3x + 2.

Long division:

                        2x^2 - 5x - 3   <-----------Quotient

                      --------------------------------------------

x^2 + 3x + 2 )     2x^4  +   x^3   -14x^2 -  19x  -  6

                          2x^4  + 6x^3 +  4x^2  

                                      -5x^3  - 18x^2 - 19x

                                      -5x^3  - 15x^2 - 10x

                                                      -3x^2 - 9x  - 6

                                                      -3x^2  - 9x - 6

                                                       .......................

2x^2 - 5x - 3 = (2x + 1)(x - 3)

So Finally,   the factors are (x + 1)(x + 2)(2x + 1)(x - 3).

Please I need help!!!!!

Answers

Answer:

Solution given:

we have

f(x)=x²-9x-36

let

y=x²-9x-36

when

x=0

y=-36

when

y=0

0=x²-9x-36

x²-12x+3x-36=0

x(x-12)+3(x-12)=0

(x-12)(x+3)=0

either

x=12

x=-3

So,

x and y intercepts are (-3,0)(12,0) and 0,-36)

please answer this question!! whoever answers correctly will get brainiest!!!

Answers

Answer:

x

=

2

Step-by-step explanation:

Answer:

Hello! answer: x = 12

Step-by-step explanation:

with these you have to cross multiply so 2 x 24 = 48 so now we know that 4 multiplied by something will equal 48 so we can simply do this by doing 48 ÷ 4 and 48 ÷ 4 = 12

Dylan draws up a plan to fence in a yard for his chickens. This distance between grid lines is 1 foot. A. Is 30 feet of fencing enough to enclose the yard?

Answers

No it definitely is not

What is the possible number of turns for a square

Answers

Answer: 5

Step-by-step explanation:

Please answer this equation 4x+1-1 > -8

Answers

Answer:

+1-1=0

4x>-8

x>-2

Step-by-step explanation:

Answer:

x>−2

Step-by-step explanation:

A bag with 10 marbles has 2 yellow marbles, 4 blue marbles, and 4 red marbles. A marble is chosen from the bag at random. What is the probability that it is yellow?

Answers

Answer:

P(Y) = 2/10 = 1/5

Step-by-step explanation:

From the above question:

Total number of marbles = 10 marbles

Number of yellow marbles = 2 yellow marbles

Number of blue marbles = 4 blue marbles

Number of red marbles = 4 red marbles.

The probability of choosing a marble that is yellow is calculated as:

= P(Y) = Number of yellow marbles/Total number of marbles

P(Y) = 2/10

P(Y) = 1/5

What is the mean of the data set? {11, 14, 15, 16, 16, 18, 20, 20, 22, 22} A. 11 B. 15.6 C. 17.4 D 18​

Answers

Answer:

C. 17.4

Step-by-step explanation:

add all the numbers and then divide  

11 + 14 + 15 + 16 + 16 + 18 + 20 + 20 + 22 + 22 = 174

then divide by the amount of numbers there is which is 10.

174/10 = 17.4

What expression is equivalent to m(n+p)

Answers

Answer:

mn + mp

Step-by-step explanation:

m(n + p) =

m(n) + m(p) =

mn + mp

Hope that helps! :)

-Aphrodite

The equivalent expression for the algebra m(n+p) is mn + mp.

What are equivalent expressions?

Equivalent expressions are similar expressions that when being solved provide the same solution. Equivalent expressions are used widely in the expansion of algebraic equations.

From the given information, we have:

=  m(n + p)

To determine the equivalent expression for the above algebraic equation, we need to expand the bracket as follows:

= m(n) + m(p)

= mn + mp

Learn more about equivalent expression here:

https://brainly.com/question/24734894

Find the volume of the solid. NO LINKS PLEASE HELP

Answers

Answer:

Use multiplication (V = l x w x h) to find the volume of a solid figure.

Step-by-step explanation:

Please help, my brain just sucks rn. The area of a rectangle is 93.6 square inches. If the length of one of its sides is 5.2 in. what is its perimeter?

Answers

46.4 inch

Step-by-step explanation:

Area=l×b

93.6 =5.2×b

93.6/5.2 =b

So b= 18

Again,

p=2(l+b)

p=2(18+5.2)

p= 2×23.2

p=46.4

What is the largest number that divides 42 and 90​

Answers

6 is the largest number that divides 42 and 90

The trapezoid shown above has an area of 21.66 square inches.

What is the total area of the shaded sections of the trapezoid?

A. 2.09 square inches
B. 4.18 square inches
C. 4.86 square inches
D. 8.74 square inches

Answers

Answer:

2.09 for only one triangle.

4.18 for two triangles.

Step-by-step explanation:

Hope this helps good luck in math if you need to look up how to find the area of a triangle all you have to do is multiply the base times the height then divide it by two.

Have a great day!

What is C26 ?

12


15


8


30

Answers

Answer:C26 is also a Category of EAD (Employment Authorization Document) provided to immigrant workers in U.S. These are dependents of H1b visa holders commonly referred to as H4-EAD.

Step-by-step explanation:

Answer:

Its 15

Step-by-step explanation:

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