All categories

2 years ago

Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.

Mathematics

1 answer:

Sophie [7]2 years ago

5 0

Answer:

The sum is 2275

Step-by-step explanation:

Given

$75,76,77....99,100$

Required

The sum

Using arithmetic progression, we have:

$S_n = \frac{n}{2}(T_1 + T_n)$

Where:

$T_1 = 75$ --- first term

$T_n = 100$ --- last term

$n = T_n - T_1 + 1$

$n = 100 - 75 + 1 = 26$

So, we have:

$S_n = \frac{n}{2}(T_1 + T_n)$

$S_n = \frac{26}{2}*(75 + 100)$

$S_n = 13*175$

$S_n = 2275$

You might be interested in

Graph y=2/3x-4<br><br><br> Plz hurry I´m trying to pass my math quiz

Lemur [1.5K]

Answer:

i believe if you open that file up you will get your answer

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

WHOEVER EXPLAINS ALL THEIR WORK AND GOES THROW EAXH STEP WILL GET BRAINLEST THAT IS COMPLETELY FINISEHD. write the equation of t

neonofarm [45]

Answer:

$y = -3x+11$

Step-by-step explanation:

I accept your challenge!

First we know that a equation of the line is a linear equation, and its equation is:

$y = mx+b$

$m: \text{slope}\\b: \text{y-intercept}$

In this context, the slope, defined as the steepness of a line is characterized as the ratio of RISE (the difference in the y-coordinates, the vertical change) over the RUN (the difference in x-coordinates, the horizontal change).

$m=\frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Once we know two points where the line goes through, we can get the slope, once we know the change in y and x.

I will take $(3,2)$ as Point 1 and $(4,-1)$ as Point 2.

So, $x_{1}=3 \text{ and } y_{1}=2\\x_{2}=4 \text{ and } y_{2}=-1$

$m=\frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}=\frac{-1-2}{4-3}$

$m=\frac{-3}{1}=-3$

Now we have to find the y-intercept:

To do so, think about the the points given and the nearly finished equation, we can find b with those two informations.

Our currently equation of the line is:

$y = -3x+b$

Using the points, take Point 1 as an example, it says that when $x = 3, y = 2$ , so plugging it in the equation:

$2 = -3(3)+b\\2 = -9+b\\11 = b$

Taking the Point 2

$-1 = -3(4)+b\\-1 = -12+b\\11 = b$

Now we found $b$ ! The equation is complete!

$y = -3x+11$

6 0

3 years ago

Ahab needs to mix 3.5 cups of liquid iced tea concentrate with 3 cups of water to make iced tea. Ahab has 21 cups of iced tea co

liraira [26]

Answer:

39 cups

Step-by-step explanation:

If we assume that the 3.5 cups of concentrate make 3.5+3 = 6.5 cups of tea, we can use the proportion ...

6.5/3.5 = x/21

to find the x cups of tea Ahab can make with 21 cups of concentrate.

Multiplying by 21, we get ...

x = 21(6.5/3.5) = 39

Ahab can make 39 cups of tea.

4 0

3 years ago

Describe the next figure in each pattern. Then draw the figure

madreJ [45]

The first figure has 3 angles, the second one has 4 angles, the third one has 5 angles so the next one will have 6 angles.

The violet figures inside stick with each side of the outer figures in the middle, so the last figure will look more less like in the attachment.

6 0

2 years ago

What is the answer of this problem -7/3(3x-2)=-21 ?

weeeeeb [17]

Answer:

= 11/3

Step-by-step explanation:

1. COMBINE MULTIPLIED TERMS INTO A SINGLE FRACTION

- 7/3 (3x-2)= -21

-7 (3x-2) = -21

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

2. DISTRIBUTE

-7( 3x- 2) ➗ 3 =-21

3. MULTIPLY ALL TERMS BY THE SAME VALUE TO ELIMINATE FRACTION DENOMINATORS

-21x + 14 ➗ 3 = 3 (-21)

4. CANCEL MULTIPLIED TERMS THAT ARE IN THE DENOMINATOR

3 ( -21x + 14) ➗ 3 (-21)

5. MULIPLY THE NUMBERS

-21x + 14 = 3(-21)

6. SUBTRACT 14 FROM BOTH SIDES OF THE EQUATION

-21x + 14 = -63

7. SIMPLIFY

-21x = - 77

8. DIVIDE BOTH SIDES OF THE EQUATION BY THE SAME TERM

-21x/-21 = -77/-21

9. SIMPLIFY

x = 11/3

3 0

3 years ago

Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.​

Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.