If k‐th term of a sequence is ak = ( -1) ^k(2-k)k/2k-1
,what is its next term ak+1 when k is even?​

Answers

Answer 1

Given:

kth term of a sequence is

[tex]a_k=\dfrac{(-1)^k(2-k)k}{2k-1}[/tex]

To find:

The next term [tex]a_{k+1}[/tex] when k is even.

Solution:

We have,

[tex]a_k=\dfrac{(-1)^k(2-k)k}{2k-1}[/tex]

Put k=k+1, to get the next term.

[tex]a_{k+1}=\dfrac{(-1)^{k+1}(2-(k+1))(k+1)}{2(k+1)-1}[/tex]

If k is even, then k+1 must be odd and odd power of -1 gives -1.

[tex]a_{k+1}=\dfrac{(-1)(2-k-1)(k+1)}{2k+2-1}[/tex]

[tex]a_{k+1}=\dfrac{(-1)(1-k)(1+k)}{2k+1}[/tex]

[tex]a_{k+1}=-\dfrac{1^2-k^2}{2k+1}[/tex]    [tex][\because (a-b)(a+b)=a^2-b^2][/tex]

[tex]a_{k+1}=-\dfrac{1-k^2}{2k+1}[/tex]

Therefore, the next term is [tex]a_{k+1}=-\dfrac{1-k^2}{2k+1}[/tex].


Related Questions

may you plz help this is due today plz i will mark you brainlist

Answers

there you go! thoose are the answers

Answer:

1 whole numbers: 15 134 -18 rational numbers:-1/3 2.4:  2 0.09, 1/9 9/10 91%: 10.5 5/4 1 1/5 100%

Step-by-step explanation:

45 WZ is parallel to XY,
SW = 15, WX = 5, SZ =12, WZ= 9 Find XY
S
I
W
Z
Х
Y

Answers

Step-by-step explanation:

wz parallel to XYXYS similar WZSXY/WZ=XS/SWXY/9=20/15XY=12

find the mean median and mode of the data set :15,11,14,10,12,15,15

Answers

Answer:

Mean = 13.14, Median = 14, Mode = 15

Step-by-step explanation:

The mean is the numbers added together divided by the number of numbers

15 + 11 + 14 + 10 + 12 + 15 + 15 = 92

92 / 7 = About 13.14

The median is the middle of the numbers ordered from least to greatest

10 11 12 14 15 15 15

14 is in the middle so that is the median.

The mode is the number showing up the most.

15 shows up 3 times so it is the mode.

Can anybody help me with this plzzz‼️
(If answer is correct i will cashapp you $6)

Answers

Step-by-step explanation:

h(x) = 3. g(x) + 5

x= -1 h(x) = 3×8 + 5= 29

x= 0h(x) = 3×5 + 5= 20

x= 2 h(x) = 3×1 + 5= 8

x= 5 h(x) = 3×-5 + 5= -10

[tex]h(x) = 3*g(x)+5[/tex]

When x = -1.

Substitute x = -1 in both h(x) and g(x).   | As shown in the table, when x = -1, g(x) = 8 |

h(-1) = 3*8+5 = 24+5 = 29

h(0) = 3*5+5 = 15+5 = 20

h(2) = 3*1+5 = 3+5 = 8

h(5) = 3*(-5)+5 = -15+5 = -10

riangle ABC is transformed using the rule (x, y) - (-x-3, y + 2). Which set of points describe triangle A'B'C'?
O A (1, 4), B'(-3,-1), C'(-1, -3)
O A (-7, 4), B' (-3,-1), C'(-5,3)
O A(-5, -2), B' (0, 2), C' (2,0)
O A' (4,4), B' (0-1), C' (2, -3)

Answers

The answer for this one would be A becuase

Answer:

b

Step-by-step explanation:

the graph shows the number of calories Natalia burned while running.
What is the slope of the line ?
What does the slope tell you ?​

Answers

Answer:

slope is y=10x.

Slope shows that she is consistently burning 10 calories per minute

Step-by-step explanation:

BRAINLIEST FOR WHOEVER GETS THIS RIGHT!!!

Answers

Answer:

56*a234 =123

a×829

h=234*234*56=2893

Find the value of 3v- 10 given that 2v- 7 = 9

Answers

Answer:

14

Step-by-step explanation:

2v - 7 = 9

Add 7 to both sides

2v = 16

Divide both sides by 2

v = 8

Plug it into 3v - 10

3v - 10 =

3(8) - 10 =

24 - 10 =

14

Answer:

14

Step-by-step explanation:

2v-7=9

2v=16

v=8

3(8)-10=14

I need helpp please​

Answers

Answer:

A, 0.07 x 0.06 =0.42.

Step-by-step explanation:

find the quotient. Problem is below

Answers

Answer:

26/9

Step-by-step explanation:

whenever you divide fractions, they turn into a multiplication problem and use the second fraction's reciprocal. so it would look something like this:

13/2 * 4/9

just do straight multiplication

numerators: 13*4 = 52

denominators: 2*9 = 18

52/18 = 26/9

Which graph represents a bike traveling at a constant rate of
12 miles per hour?

Answers

Answer:

what graph?...........

While practicing her foul kicks for soccer, Louisa made 85% of her shots. If she made 51 shots, how many shots did she kick in total?

Answers

Answer:

the exact answer is 58.65

Step-by-step explanation:

since she made 85% of her shots, that means in total from her 51 shots, she made 115% more than 51 (you add 15% to 100%). The 15% is from the difference of 100% and 85%. You then change 115% to fraction form (1.15) and multiply it by the amount of shots made, getting you 58.65. Since you can't make a fraction in terms of a real life scenario like this, you prob need to round or something. Diff teachers want diff things

The answer is 60 because you would do 100 divided by 85 multipled by 51

But his teacher that he needed to measure the height of a building in which his classroom is located he backs away from the building and places a mirror on the ground between him and the wall when he can see the top of the building in the mirror Peter is 2‘9“ away from the mirror and the mirror is 11 feet away from the wall of the building Peter knew his eye level was exactly 5‘6“ off the ground so he was able to calculate the height of the building how tall is the building in feet

Answers

Answer:

IT'S 22 JUST FOUND OUT

Step-by-step explanation:

Help! I need help asap

Answers

Answer:

3 looks right but I am not so sure

Step-by-step explanation:

sorry if i am wring

A. 1
B. .5
C. .55
D. .10
E. 1.10

Answers

Answer:

E

Step-by-step explanation:

The onlt one that makes sense

E is the correct answer . Hope u got it correct

Write 24 as a product of primes.
Use index notation when giving your answer.​

Answers

Answer:

2^3 * 3

Step-by-step explanation:

Here are the first several prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23

To find the prime factorization of a number, start by dividing the number by the smallest prime number it is divisible by. Keep dividing by that prime number until you can't anymore. You only divide by prime numbers that divide evenly. Then move on to the next prime number that divides evenly, and do the same. You eventually will get to 1. Then you put together all the prime factors.

This is much easier to do than it sounds like in this explanation.

Start with 24.

24/2 = 12

12/2 = 6

6/2 = 3    3 is not divisible by 2, so we move on to 3.

3/3 = 1    We got to 1, so we are done.

The prime factorization is the product of all the prime numbers we divided by which are in bold.

24 = 2 * 2 * 2 * 3

Now we index it:

24 = 2^3 * 3

Can someone plz help me

Answers

Answer:

Step-by-step explanation:

because the two lines are not unique.. in other words they lay on top of each other.. they have many solutions and we can't determine price  .. so answer C

Please help
I will mark brainlest and theres alot of points :)

Answers

Answer:

answer is a

Step-by-step explanation:

5(2)=10+2(7)=24

if f(x)=5x-12, what is f(2)?

Answers

Answer:

Step-by-step explanation:

5x2-12=10-12=-2

Answer:

=-2 ( B.)

Step-by-step explanation:

f(x) = 5x-12

f(2)= 5(2)-12

=10-12

=-2

I hope helps you and if you want and consider you can give me a Brainly crown

Find the average rate of change of the function f(x)=(3/-3x-5), on the interval x ∈ [0,3]

Answers

Answer:

9/70

Step-by-step explanation:

Mathematically;

Average rate of change on an interval [a,b] is;

f(b) - f(a)/b-a

f(0) = -3/5

f(3) = -3/14

a = 0

b = 3

Making the substitution, we have

-3/14-(-3/5)/3-0

= 3/5-3/14/3

= (42-15)/70/3

= 27/70/3

= 27/70 * 1/3 = 9/70

Is the equation linear or non-linear?

2x-2y=18

Answers

It’s a non-linear equation

Can you some please help me with this ASAP!!!

Answers

Answer:

slope is 0

Step-by-step explanation:

to find slope y2 - y1 / x2 - x1

(6, -2) and (12, -2)

-2 - (-2) / 12 - 6

= -2 + 2/6

= 0/6

= 0

Answer:

slope is 0

Step-by-step explanation:

Help!!! Whats The answer, Please explain your answer Marking brainlliest:D......

Answers

the answer would be 96 square feet length

6 x (4)^2 = 96

-3х - y + 4 = 28
2х - 3y+ 2 = 2
3х - 2y + 2 = 2
Solve each system by elimination

Answers

Answer:

x=-72/11 y=-48/11

Step-by-step explanation:

yw !

Which of the following can be used to prove that triangle ABC is congruent to triangle DEF?

Answers

Answer:

SAS congruence theorem

Step-by-step explanation:

since we are given the two congruent sides and the right angle. We know all right angles are congruent and the right angle is an angle that is between the two sides which is why it is SAS. hope this helps :))

The ruler below shows a 7-inch segment divided into 2 equal parts. What is the length of one of those parts?

Answers

Answer:

3.5

Step-by-step explanation:

7/3= 3.5 or 3 1/2

8^1/6 multiply 2^x = 32^1/2 Work out the exact value of x. WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!!

Answers

Answer:

x=2

Step-by-step explanation:

8^1/6 x 2^x = 32^1/2

Divide by 8^1/6

2^x= 32^42/8^y6

2^x=4

but 4= 2^2

2^x= 2^2

x=2

I hope helps you and if you consider and want you can give me a Brainly crown

Answer:

[tex]\huge\boxed{x=2}}[/tex]

Step-by-step explanation:

[tex]8^\frac{1}{6}\cdot2^x=32^\frac{1}{2}\\\\(2^3)^\frac{1}{6}\cdot2^x=(2^5)^\frac{1}{2}\qquad|\text{use}\ (a^n)^m=a^{nm}\\\\2^{3\cdot\frac{1}{6}}\cdot2^x=2^{5\cdot\frac{1}{2}}\\\\2^{\frac{1}{2}}\cdot2^x=2^\frac{5}{2}\qquad|\text{use}\ a^n\cdot a^m=a^{n+m}\\\\2^{\frac{1}{2}+x}=2^\frac{5}{2}\iff\dfrac{1}{2}+x=\dfrac{5}{2}\qquad|\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\x=\dfrac{4}{2}\\\\x=2[/tex]

Divide the following polynomial expression.

(n^4 +5n^3+9n^2) / 9n^3

Answers

Dhjdjdjdjdjdjndjdjdjdjdjdjjsjdjdjdjd

2(x-5)=10 but the pemdas is backwards

Answers

Answer:

2 (x-5) = 10

2x-10 = 10

2x = 10 + 10

x = 20/2

x = 10

Step-by-step explanation:

Solve Each Equation

5. -8(5+4x)=-232

6. -84=4(4r+7)

Answers

Step-by-step explanation:

5.

[tex] - 8(5 + 4x) = - 232[/tex]

[tex] - 40 - 32x = - 232 \\ - 32x = - 232 + 40 \\ - 32x = - 192 \\ \frac{ - 32x}{ - 32} = \frac{ - 192}{ - 32} \\ \\ \huge x = 6[/tex]

6.

[tex] - 84 = 4(4r + 7) \\ - 84 = 16r + 28 \\ 16r = - 84 - 28 \\ 16r = - 112 \\ \frac{16r}{16} = - \frac{112}{16} \\ \\ \huge r = 7[/tex]

Hope this helps you

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