t is an number in the series: 1/t + 3/t + 5/t + ...+ t-1/t a)Determine the number of terms in the series in terms of t. b)Determine the sum of the series in terms of t. c)Hence,or otherwise,evaluate:(1/4+3/4)+(1/6+3/6+5/6)+(1/8+3/8+5/8+7/8)+...+(1/50+3/50+5/50+49/50)​

Answers

Answer 1

Answer:

Below in bold.

Step-by-step explanation:

1/t + 3/t + 5/t +  ...+  t-1/t

This is an arithmetic series in which the common difference is 2/t.

a) The number of terms = [ (last term - first term) / common difference] + 1

=  [(t-1)/t - 1/t) / 2/t]  + 1

= (t - 2)/t * t/2 + 1

= (t -2)/2 + 1

= (t-2) / 2 + 2/2

= t/2.

b). Sum of the series (n/2)(a + l)  where a = first term , n = number of terms and l = last term, so

Sum = (t/2)/2 ( 1/t + (t-1)/t)

= t/4 * 1

= t/4.

c). (1/4+3/4 )+ (1/6+3/6+5/6 )+( 1/8+3/8+5/8+7/8) +...+(1/50+3/50+5/50+49/50)​

Using the results from a) and b):

The sum = 4/4  + 6/4 + 8/4 + ......+ 50/4.

= 1 + 1.5 + 2 +...... + 12.5

This is an AS  with common difference = 0.5,

Number of terms = [(12.5 -1) / 0.5] + 1

= 23 + 1

= 24, so

Sum = (24/2)(1 + 12.5)

=  12  * 13.5

=  162.

Answer 2

The number of terms is t/2, and the sum of the series is 1/2 - (t - 2)/4

What is an arithmetic sequence?

In an arithmetic sequence, the common difference is the difference between successive terms.

a) From the sequence:

a = 1/t; d = (3/t) - (1/t) = 2/t

The number of terms is:

(t - 1)/t = 1/t + (n - 1)(2/t)

t - 1 = 1 + 2(n - 1)

t = 2n

n = t/2

b) The sum of the series is:

S = (n/2)[2a + (n - 1)d]

S = (t/2/2)[2(1/t) + (t/2 - 1)(2/t)]

S = (t/4)[2/t - (t - 2)/t]

S = 1/2 - (t - 2)/4

The number of terms is t/2, and the sum of the series is 1/2 - (t - 2)/4

Find out more on arithmetic sequence at: https://brainly.com/question/6561461


Related Questions

BRAINLIEST

Plot the following co-ordinates and find the fourth point D to make a square A (-1,3) B (1,-1) C(5,1).

Once you have found the missing coordinate use pythagoras to calculate the length of the sides.

Answers

Answer:

Next coordinate is (-1,-3)

Step-by-step explanation:

draw a graph in graph paper and mark all coordinates

In order to solve an equation like `1.77x=52` I would.....
(Include steps plz)

Answers

Answer:

Divide each term by 1.77 and simplify.

52/1.77

Move the seven underneath the 52 and leave the x on one side.

x = 29.37853107

Step-by-step explanation:

x3 - 3x^2- 54x + 112

Answers

Answer:

(x -2) (x- 8) (x+7)

Step-by-step explanation:

Alison has a goal of saving $50. She has saved $31 so far. What percentage of her goal has she saved?

Answers

Answer:

62%

Step-by-step explanation:

Identify each graph as being a non-linear function, linear function, or not a function.
Explain your choices.
Graph A
Graph B
Graph C
3
3
2
4 +
2
I
1
3
1+
2+
++
2 3 x
-3 -2
-2
-1
1
1
2 3 3
1+
TS
-1
-1
1

Answers

Graph B is the answer

nd carefully click on the appropriate answer choice. It will mark the answer with a blue dot. (It will look like a target)
1. A rectangle made of square tiles measures 8 tiles long and 5 tiles wide.
What is the length of a similar rectangle whose width is 10 tiles?
A 18 tiles
B 16 tiles
C 14 tiles
D 10 tiles

Answers

B 16 because we see 5x2=10 so the length would be 8x2=16

what is 0.71+0.9 equal too

Answers

Answer:

0.71+0.9=1.61 is your answer

0.71 + 0.9

0.9 = 0.90

   0.17

+ 0.90

----------

   1.61

Someone ppl ease help meeeee. Match them

Answers

Answer:

Step-by-step explanation:

2/5 is 0.4

0.75 is 3/4

5/8 is 0.625

0.875 is 7/8

2/5=0.4

0.75=3/4

5/8=0.625

0.875=7/8

how do I do this question​

Answers

Answer:

(2,11)

Step-by-step explanation:

May someone help, please?

Answers

Answer:

A, C, and E are true

how can I solve this problem ?

(x³-2x²-2x+1)(x-1)​

Answers

x^2(x-2)(-2x+1)(x-1)

how:

(x³-2x²-2x+1)(x-1)​

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

x^2(x-2)(-2x+1)(x-1)

YALL PLS HELP which of these choices are equivalent to the quotient below check all that apply square root of 100 over the square root of 20

Answers

Answer:

√5, √15/√3, √25/√5

A.

C.

D.

Step-by-step explanation:

A P E X

COUNTING RISE OVER RUN
COUNT THE RISE OVER RUN AND SIMPLIFY IF POSSIBLE TO DETERMINE THE
SLOPE OF CACH LIME. THEN, ORDER YOUR ANSWERS (AND THE LETTER OF THE
GRAPH) FRON GREATEST TO LEAST TO CREATE YOUR CODE WORD.

Answers

Answer:

P) slope of 3, L) slope of 1, U) slope of 1/4, and S) slope of -1

Step-by-step explanation: Start at (0,0) and go to your next point

P) its rise 3 and runs 1  slope = 3

S) t rise 1 and runs back 1, slope =  -1

U) it rise 1 and runs 4 slope = 1/4

L) its rise 1 and runs 1 slope = 1

Now in order of greatest to least

I NEED HELP ASAP!!!!!

Answers

It’s 3/10 if it’s not then do 28

Answer:

3/10

Step-by-step explanation:

28 + 12 = 40 tokens

28 are black     28/40 = 7/10 = 70%

12 are white    12/40 = 3/10 = 30%

Therefore,the most logical answer I see is 3/10.

What is the approximate volume of the cone that is 9 cm in height and 15 cm as a radius use 3.14 for pi

Answers

Answer:

2120.58

Step-by-step explanation:

Answer:

The volume of a cone is pi multiplied by the radius squared times the height divided by three.

Step-by-step explanation:

If 3.14 is used for pi:

V = 3.14 * 15^2 (9/3)

   = 3.14 * 15^2 (3)

   = 3.14 * 225 * 3

   = 706.5 * 3

   = 2,119.5 cm cubed

If 3.14 is not used for pi:

V = pi * 15^2 (9/3)

   = pi * 15^2 (3)

   = pi * 225 * 3

   = 706.8583470577035 * 3

   = 2,120.57504117311 cm cubed

            If helpful, please mark as brainliest! =)

HELP I NEED THIS BY TONIGHTTT

Giancarlo wants to buy a new laptop.
• Last week Best Buy had a laptop on sale for $425.00.
• This week the laptops were marked up to $500.00.
Find the percent of increase in the price of the laptops. Round your answer to the tenths place.

Answers

the answer is my love

HELP ME PLEAS EILL GIVE BRAINLY!!!!!!

Answers

Answer:

4

Step-by-step explanation:

point is -2,4

That would be 4
Points: -2,4
Hope this helped

goldennnjoyyy avatar
goldennnjoyyy
Yesterday
Mathematics
High School
(PLEASE HELP GIVING BRAINILEST)
In training for a swim meet, Logan swam 750 meters in 1/3​ of an hour. His swimming partner, Mila, swam 2/3 of Logan's distance in 1/4​ of an hour.
Fill in the blanks to compare Mila's and Logan’s swimming speeds.

1. What is Logan's average swimming speed? Show your work.

Write your answer in the space below.





2. What is Mila's average swimming speed? Show your work.

Write your answer in the space below.





3. Compare Mila's and Logan’s swimming speeds. You must do something more than just state the speeds. Show your work.

Write your answer in the space below.

Answers

Answer:

1. Logan's Average speed is 2.25 kilometers per hour.2. Mila's average swimming speed is 34.44 m/min.3. His average speed was 3 times 750 meters per hour, which is 2250 meter per hour, or 750 OVER 20 = 37.5 meters per minute.

Step-by-step explanation:

i hope it helps :)

Answer:

See below

Step-by-step explanation:

Speed = distance/time

1. Logan swam 750 meters in 1/3 of an hour

Logan's speed is:

s = 750 : 1/3 = 750*3 = 2250 meters /hour

2. Mila swam 2/3 of Logan's distance:

2/3*750 = 500 metersTime is 1/4 of an hour

Mila's speed is:

s = 500 : 1/4 = 500 * 4 = 2000 meters/hour

3. The difference is:

Logan is faster by: 2250 - 2000 = 250 meters/hour

I do not understand this LOL someone help

Answers

Answer:

a reflection over the y axis

Step-by-step explanation:

A garden has four sides that are all the same length. Each side measures x+ 4 units. The gardeners perimeter is 112 units. WHat is the value of x

Will mark brainliest for the fastest answer

Answers

Answer:

24

Step-by-step explanation:

So basically just do 112 divided by 4 to find the length of each side. Then from there minus that one side by 4 to get what you need x to be to be the length of the one side. One side is 28. Also...

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2-3x=-x-8





^'fusgwowjisbsjwbw
b​

Answers

Answer:

2-3x=-x-8

+3x+8 both sides

2+8=3x-x

10=2x

/5 both sides

x=5

4 (10-x) = 8x + 4
What is x?

Answers

Answer:

3 = x

Step-by-step explanation:

4 (10-x) = 8x + 4

Distribute

40 -4x = 8x+4

Add 4x to each side

40 -4x+4x = 8x+4 +4x

40 = 12x+4

Subtract 4

40 -4 = 12x+4-4

36 = 12x

Divide each side by 12

36/12 = 12x/12

3 = x

19. A cylinder with a radius of 0.28 m and
a length of 7 m is to be replaced with a
cylinder of radius 0.25 m. The volume
must remain the same. How long must
the new cylinder be? Give your answer
to the nearest hundredth of a metre.

Answers

Answer:

0.26

Step-by-step explanation:

Answer: Mark me brainliest..

Step-by-step explanation: and imma put the answer inside the comments if you do so. youve got nothing to lose! :D

Please help me with the questions please ASAP please please ASAP ASAP please please help please ASAP please please help please please
I’ll mark you as a brnlist please

Answers

Answer:

x=24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

3x+10=x+58

2x=48

x=24

help me ASAP!!!!!! Please

Answers

I believe the anwser to be 15cm
69.28 :)
you wanna start by plugging in what you know.
a^2+65^2=95^2

now simplify.
a^2+4,225=9,025

[subtract 4,225 from both sides]
a^2=4,800

get a by itself by doing the opposite. [square root both sides]
a=69.28

hope this helped!

HELP PLS I NEED AN ANSWER FAST

Answers

Step-by-step explanation:

[tex]y = a {b}^{x} \\ b = \frac{0.0006}{0.006} = 0.1 \\ a = 6 \\ y =6 \times {0.1}^{x} [/tex]

1. Mr. Gunny deposits $4,900 in a savings account that pays 1.5% interest compounded
quarterly.

A1. Find the first quarter's interest.

A2. Find the first quarter's balance.

C. Find the second quarter's interest

D. Find the second quarter's balance.

E. Find the third quarter's interest.

F. Find the third quarter's balance.

Answers

Answer:

a) 18.38

b) 4918.38

c) 18.44

d) 4936.82

e) 18.51

f) 4955.33

Step-by-step explanation:

Given

A [tex]= 4900[/tex]

r [tex]= \frac{1.5}{100} =0.015[/tex]

m [tex]= 4[/tex]

a)

I1

[tex]= 4900 *( 1 +\frac{0.015}{4})^{4 *\frac{3}{12}} -4900\\= 4918.38-4900\\= 18.38[/tex]

b) [tex]4918.38[/tex]

c)

[tex]= 4918.38 *( 1 +\frac{0.015}{4})^{4 *\frac{3}{12}} -4918.38\\= 4936.82-4918.38\\= 18.44[/tex]

d) [tex]4936.82[/tex]

e)

[tex]= 4936.82 *( 1 +\frac{0.015}{4})^{4 *\frac{3}{12}} -4936.82\\= 4955.33-4936.82\\= 18.51[/tex]

f) [tex]4955.33[/tex]

Im such an idiot for not paying attention in class but someone help PLEASE the assignment is due at 3:05 and its 2:50

Answers

Answer:

Help with what?


Enrique bought a packing tube to ship a poster to his cousin. If the packing tube had a volume of 1761 cubic centimeters and
an altitude of 11 centimeters, what was the radius of the packing tube?

a.) 16 cm
b.) 12 cm
c.) 7 cm
d.) 4cm

Answers

Answer:

r = 7 cm

Step-by-step explanation:

Given that,

Volume of the packing tube, V = 1761 cm²

The altitude of the tube, h = 11 cm

We need to find the radius of the packing tube. The volume of the the cylindrical shaped object is given by :

[tex]V=\pi r^2 h\\\\r^2=\dfrac{V}{\pi h}\\\\r^2=\dfrac{1761}{\pi \times 11}\\\\r=7.13\ cm[/tex]

or

r = 7 cm

So, the radius of the packing tube is 7 cm.

An object is traveling at a steady speed of 8 2/3 miles per hour. How long will it take the object to travel to 5 1/5 miles If the object reduces its speed by `\frac{1}{2}`, what is its speed? If the object reduces its speed by 30%, what is its speed after the reduction?

Answers

Answer:

3/5 hour

4 1/3 miles per hour

6 1/15 miles per hour

Step-by-step explanation:

Given that the object is travelling at a steady speed of 8 2/3 miles per hour and covers  5 1/5 miles

Recall that distance  = speed * time

hence

5 1/5 miles =  8 2/3 miles per hour * time t

26/5 = 26/3 * t

Multiply both sides by 3/26

26/5 * 3/26 = t

t = 3/5 hour

If the object reduces its speed by 1/2, the new speed

= 1/2 * 8 2/3 miles per hour

= 1/2 * 26/3

= 13/3 miles per hour

= 4 1/3 miles per hour

If the object reduces its speed by 30%, the new speed

= 8 2/3 miles per hour - 30% * 8 2/3 miles per hour

= 0.7 * 8 2/3 miles per hour

= 7/10 * 26/3

= 91/15

= 6 1/15 miles per hour

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