the common diiference of an ap is 4 . the last term is 72 and the sum of all terms is 600. find the first term and the number of terms​

Answers

Answer 1

Answer:

a = - 24 ; n =25

a = 28 ; n = 25

Step-by-step explanation:

n = l - a/d + 1

d = common difference = 4

Last term = l = 72

n = 72 - a/4 + 1

4n = 72 - a + 4

4n = 76 - a

a = 76 - 4n - - - (1)

Sum of terms :

Sn = n/2(a + l)

Sn = 600

600 = n/2(a + 72)

1200 = n(76-4n +72)

1200 = 148n - 4n

4n² - 148n + 1200

Solving the quadratic equation :

Roots of n are :

12 and 25

From (1)

n = 12

a = 76 - 4(12) = 28

n = 25

a = 76 - 4(25) = - 24

Hence,

a = - 24 ; n =25

a = 28 ; n = 25


Related Questions

Lisa rolls a number cube that has sides labeled 1 to 6 and then flips a coin. What is the probability that she rolls an odd number and flips tails?

A.1/8

B.1/4

C.1/2

D.3/4

Answers

Answer: B. 1/4

Step-by-step explanation: The probability of rolling an odd number is 3/6 since there are 3 odd numbers between 1 and 6 (1, 3, 5). The probability of flipping a coin and getting tails is 1/2 since you can either get heads or tails. With this knowledge, you must multiply these two probabilities to get the probability of getting an odd number AND tails; so, 3/6 x 1/2 = 3/12 = 1/4.

Complete the ratio table.
15
14
42
60
56
75
70
90

Answers

-1 because I need the points

What is the equation of the line that passes through the point (6,6) and has a slope of 5/3??​

Answers

Answer:

y = 5/3x - 4

Step-by-step explanation:

(6, 6)

m = 5/3

Slope-intercept:

y - y1 = m(x - x1)

y - 6 = 5/3(x - 6)

y - 6 = 5/3x - 10

y = 5/3x - 10 + 6

y = 5/3x - 4

Which choice is an irrational number?

A.
4
π
π

B.

6
2

C.

18

D.
21
.
989

Answers

Answer:

3 one good luck with the question

Answer:

dddddddddddddddddddddddddd

Jennifer's grandma bought her a $50 savings bond when she was born. When Jennifer is 30 years old, the bond will have earned 110% in interest. How much will the bond be worth when Jennifer is 30 years old?​

Answers

Answer:

105$

Step-by-step explanation:

We are told that she starts with 50$

We are also that after 30 years she earns 110% on interest

Given this information we need to find the value of the bond after the 30 years

To do so we take 110% of the initial value (50$) and add that to the initial value

So the answer = 110%(50) + 50

110%*50=55

55+50=105

So in 30 years the bond will be worth 105$

Alan has read 20% of his book. He has 64 more pages to finish. How many pages are there in the​ book?

Answers

Answer:

80 pages

Step-by-step explanation:

We can think of this as 80% of the book is 64 pages

.8x = 64

x=80

he read 80 books total

Help ASAP PLS! 20 Points:) I am reporting any fake responses so please be for real, I appreciate it!
The population of a species of starfish in the Gulf of Mexico is decreasing at an exponential rate, A(t) = A0e(kt) . Five years ago the population was 10,000. The current population is only 2000. When the population is 500, the starfish population cannot recover. When will this event occur?

Show your work and explain the process of solving this problem.

Answers

Answer: 4.3 years
Explanation:

Ava's watering can holds 2 liters of
water. She uses 200 milliliters to
water each of her plants. How many
plants can she water if she use the
entire watering can? (uh i’m about to get 0 ‍)

Answers

Answer:

2,000 m (2 Liters) = 100 plants

Step-by-step explanation:

2,000 milliliters make up 2 liters.

200 liters are being poured.

2,000/200 = 10

10 plants are being watered each time.

200 m = 10 plants

400 m = 20 plants

600 m = 30 plants

800 m = 40 plants

1,000 m = 50 plants

1,200 m = 60 plants

1,400 m = 70 plants

1,600 m = 80 plants

1,800 m = 90 plants

2,000 m = 100 plants

Let me know if this helps!

Rewrite 1401/8
in radical form.

Answers

Answer:

We can write  

140 / 1 /8

in radical form as:  

8 √ 140

Step-by-step explanation:

What is the answer to equation
-3× + 7 =1

Answers

Answer:x=2

Step-by-step explanation:

The equation 3x – 2y = 18 is in slope intercept
form.
If the y variable was isolated, it would be in
What
form.
(Use all lowercase letters when writing the answers)

Answers

Answer:

Y intercept form

Step-by-step explanation:

2. How much will a $210 bicycle on sale for 15% off cost?
$195.50
$31.50
$178.50
O $241.50

Answers

The answer is $178.50

Answer:

The answer would be $178.50

Step-by-step explanation:

Complete the table of values for y = -2x + 11

Can you help? ​

Answers

Answer:

x  0  1  2  3  4

y  11  9 7  5  3

Step-by-step explanation:

basically you just plug in all of the x values shown in the table into the equation, to find the matching y values.

i hope this helps :)

PWEASE HELP I DON'T UNDERSTAND THIS

Answers

Answer:1) 76m

2) 239 cm

Step-by-step explanation:

The difference of two numbers is 4. Their sum is 24.what are the numbers?

Write equation

Answers

Answer:

x = 14 and y = 10

Step-by-step explanation:

TRANSLATING WORDS INTO EQUATIONS:

Let the two numbers be x and y  

"The sum of two numbers is 24" translate as x + y = 24  

"Their difference is 4" translates as x-y=4

Those two equations make up the system of linear equations

SOLVING BY ELIMINATION:

Adding the two equations, we get

x + y + x - y = 24 + 4

2x = 28

x = 28 / 2

x = 14

substituting that into x + y = 24 we get

14 + y = 24

y = 24 - 14

y = 10

hope it helps :)

(will give brainly) orde the values on the cards below in ascending order

Answers

Answer:

Step-by-step explanation:

Set 1

first of all we have to look at the negative numbers:

-99% = -0,99

-√80 = is almost 9

so :

-9,(9) ; -√80 ; -99%

then the positive numbers:

19% = 0,19

√9 = 3

1/9 = 0,11...

so

1/9 ; 19% ; √9

final answer:

-9,(9) ; -√80 ; -99% ; 1/9 ; 19%, √9

Set 2

descending order = from greatest to least

In this case we have to look at first at positive numbers

2/3 = 0,6

√23 = 4,...

20/3 = 6,...

23% = 0,23

so

20/3 ; √23 ; 2/3 ; 23%

negative numbers

-√34 = -5,...

so :

-4,(3) ; -√34

final answer:

20/3 ; √23 ; 2/3 ; 23% ; -4,(3) ; -√34

6m - 8 = 1/2(-4m + 16)

Answers

Answer:

m=2

Step-by-step explanation:

6m - 8 = 1/2(-4m + 16)

Distribute

6m -8 = -2m +8

Add 2m to each side

6m-8+2m = -2m +8+2m

8m -8 = 8

Add 8 to each side

8m-8+8 = 8+8

8m = 16

Divide each side by 8

8m/8 = 16/8

m=2

Kurt and Maria's high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached. Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2. Maria estimated the number of pounds of newspapers collected by finding One-fifth of 3,600.

Answers

Options:

Who is right, and why?

a. Neither Kurt nor Maria is right, because 3,500 should be used instead of 3,600.

b. Kurt is right, because finding 1/5 of 3,600 is not a good way to approximate 21% of 3,585.

c. Maria is right, because finding 10% of 3,600 and multiplying the result by 2 is not a good way to approximate 21% of 3,585.

d. Both Kurt and Maria are right, because 3,585 should be rounded up to 3,600, and 21% of this amount can be approximated by either finding 10% of 3,600 and multiplying the result by 2 or by finding 1/5 of 3,600.

Answer:

d. Both Kurt and Maria are right, because 3,585 should be rounded up to 3,600, and 21% of this amount can be approximated by either finding 10% of 3,600 and multiplying the result by 2 or by finding 1/5 of 3,600.

Step-by-step explanation:

Given

[tex]Goal = 3585[/tex]

[tex]Collected = 21\%[/tex]

[tex]Kurt= 10\% * 3600 * 2[/tex]

[tex]Maria = \frac{1}{5} * 3600[/tex]

Required [Missing from the question]

Who is correct and why?

First, we calculate the actual amount collected.

[tex]Actual = Collected * Goal[/tex]

[tex]Actual = 21\% * 3585[/tex]

[tex]Actual = 752.85[/tex]

[tex]Actual = 753[/tex] --- approximate

Next, determine the estimate (round 3585 to 3600 and 21% to 20%)

[tex]Estimate = 20\% * 3600[/tex]

[tex]Estimate = 720[/tex]

Next, calculate Kurt and Maria's estimates

[tex]Kurt= 10\% * 3600 * 2[/tex]

[tex]Kurt = 720[/tex]

[tex]Maria = \frac{1}{5} * 3600[/tex]

[tex]Maria = 720[/tex]

Hence, Kurt and Maria are correct because of option (d)

Answer:

d

Step-by-step explanation:

Find the radius of a circle with a circumference of 18.84 m. Use 3.14 for ​.

Answers

Answer:

2.9

Step-by-step explanation:

if you need me to explain just comment!

I hope i was able to help!!!!!

Answer: 3m

Step-by-step explanation:

c = 2[tex]\pi[/tex]r

18.84 = 2 x 3.14r

18.84 = 6.28 r

r = 3

What is the ?, help please

Answers

Step-by-step explanation:

According to the base of similarity, then

12÷6=8÷x

12x=48

=4

6+4=

10

what is equivalent to 7⁶​

Answers

42 is then answer, 7x7x7x7x7x7=42

Hope it helps

Brainliest please
42 IS NOT THE ANSWER.

The answer is 117,649

For her birthday party, Kelly invited her friends to a nearby roller-skating rink. The area of the rectangular rink is 1,530 ft2, and the length is 51 ft. What is the width of the rink?

Answers

Answer:

30ft

Step-by-step explanation:

1530ft2 divided by 51ft.

The product of 7 and b is less than -35.
HELP ASAP

Answers

7b < -35
b < -5
.............,....,.

Can someone plz help me I’m really confused on this.

Answers

Answer: x:6

y:7

z:6

Step-by-step explanation:

Answer:

x = 5.25

y = 6

z = 5.25

Step-by-step explanation:

For x and z

x = z

3      x

---- = ----

4       7

Cross multiply: 21 = 4x

21/4 = x

x = 5.25

z = 5.25

For y

3       y

---- = ----

4       8

Cross multiply: 24 = 4y

24/4 = y

y = 6

44 is r% of 16 what is r

Answers

Answer:

r= 275

Step-by-step explanation:

Let's write an equation with the given information.

44= r% ×16

Rewrite the percentage as a fraction:

[tex]44 = \frac{r}{100} \times 16[/tex]

Divide both sides by 16:

[tex] \frac{r}{100} = 44 \div 16[/tex]

[tex] \frac{r}{100} = 2.75[/tex]

Multiply both sides by 100:

r= 2.75(100)

r= 275

how do I solve this?? number 8

Answers

Answer:

135

Step-by-step explanation:

that line equals 180 degrees so just subtract 45 to get the value of x

To get the correct answer to this problem you must subtract 45 to get your answer

Trent attaches his A+ test to the refrigerator with a circular magnet. Out of curiosity, he measures the magnet and calculates that it has a diameter of 4 centimeters. What is the magnet's area?

Answers

Answer:

12.6 cm²

Step-by-step explanation:

From the above question, the magnet is circular in shape

The area of a circle is given as:

= πr²

The area of the magnet = π × r²

Diameter = 4cm

r = Diameter/2 = 4cm/2 = 2cm

= π × (2cm)²

= 12.566370614cm²

Approximately = 12.6 cm²

The area of the magnet = 12.6cm²

Mhanifa please help im almost done! I will mark brainliest :)

Answers

Answer:

Hello! Your answer is, 1 :A)28 AND 2:D)75 and CD AND 3:B)10 1/2

Step-by-step explanation:

Hope I helped! Brainiest plz!♥ Have a nice afternoon. Hope you make a 100%! -Amelia

Answer:

#5

x/ 12 = 7/3 x = 12*7/3x =  28 feetOption A

#6

Consider letter position in names of figures:

A. QR and CD is the correct one

#7

x/ 8 = 7/12x = 8*7/12x = 4 2/3

One angle marked and one angle congruent as vertical

A. AA postulate; 4 2/3 is the correct option

1 oz = 16 lb
What is 24 ounces converted to pounds?
Write your answer as a fraction in simplest form. 1)
24 ounces is equal to
pounds.

Answers

Answer:

1.5 pounds

Step-by-step explanation:

24-16 is 8, so divide 8 by 16 and you get 1.5

The value of 24 ounces to pounds is 1.5 pounds.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that 1 oz is equal to 1/16 pound. The value of 24 ounces to 16 pounds will be calculated as,

1 oz = 1/16 pounds

24 oz = 24 / 16

24 oz = 1.5 pounds

Hence, the value of 24 oz is 1.5 pounds.

To know more about an expression follow

https://brainly.com/question/25490005

#SPJ2

Given the sequence 9,6,3,0,..., at what nth term will the number become -24?

Answers

Answer:

12

Step-by-step explanation:

A sequence is given and we need to find the term when it will become -24 . The given sequence is,

9 , 6 , 3 ,0 , . . . . .

Here Common Difference can be calculated by subtracting consecutive terms . So the Common Difference is 6-9 = -3 . Here the nth term is (-24) .Now using the formula to find nth term .

⇒ T_n = a + (n-1)d

⇒ (-24) = 9 + (n-1)(-3)

⇒ -24-9 = (n-1)(-3)

⇒ (n-1) = -33/-3

⇒ n-1 = 11

⇒ n = 11 + 1

⇒ n = 12

Hence the required number of term is 12.
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