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valkas [14]
2 years ago
11

Find the sum of the first 7 terms of the following series, to the nearest integer. 150,60,24...

Mathematics
2 answers:
Kazeer [188]2 years ago
6 0

Answer:

  250

Step-by-step explanation:

The sum of the terms of a geometric series is given by the formula ...

  Sn = a1×(1 -r^n)/(1 -r)

sum of n terms for first term a1 and common ratio r.

__

<h3>series sum</h3>

The given series has first term a1 = 150, and common ratio r = 60/150 = 2/5. Putting these values into the formula gives a sum of 7 terms that is ...

  S7 = 150×(1 -(2/5)^7)/(1 -2/5) = 150((77997/78125)/(3/5))

  S7 = 150×(25999/15625) = 249.5904

Rounded to the nearest integer, the sum of the first 7 terms is 250.

Sonja [21]2 years ago
4 0

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The sum of the first seven terms of the series is 249.

<h3>What is geometrical series?</h3>

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

The given series is an geometric series, the details of the series are:

a₁ = 150

r = 60/150 = 0.4

n = 7

The sum of the geometric series is,

S = 150(1-0.4⁶)/(1-0.4)

S = 248.976 ≈ 249

Hence, the sum of the first seven terms of the series is 249.

Learn more about Geometrical Series:

brainly.com/question/4617980

#SPJ1

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(3x-5) (7x+5) find x
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Answer:

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Step-by-step explanation:

3x-5+7x+5+90=180

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70% of the 100 students in a middle school cafeteria bought their lunch. Some of the students that bought there lunch leave the
Fittoniya [83]
600 because 60 percent of 100 is 600
5 0
3 years ago
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Una recta atraviesa el punto (4,-6) Y tiene una pendiente igual a 5/4
yulyashka [42]

Answer:

y=5/4x-11

Step-by-step explanation:

tenemos un punto (4,-6) y una pendiente equal a 5/4.

usa la ecuación y=mx+b (m es la pendiente, b es el y interceptar)

porque sabemos la pendiente es 5/4, ahora mismo la ecuación es:

y=5/4x+b

en el punto, x=4, y=-6

podemos sustituir los números en la fómula para resolver b

-6=4(5/4)+b

-6=5+b

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entonces,

la ecuación de la recta es y=5/4x-11

(¡lo siento mi español no es perfecto!)

8 0
3 years ago
HELP ME PLEASE!! Urgently needed!!!
elixir [45]
The equation for the first part would be 4.50p+40=112.
This is because he earns 40 dollars in wages which doesn't change but the number of shoes he commissions, which would be 4.50 per pair. varies based on how many he commissions.

The answer to your second part would be 16.
To find the number, you subtract 40 from each side which gets you 4.50 = 72. From there you just divide which gets you 16.

Another easy way to do it would just be substituting until you find the right number like on a calculator but if you don't have a calculator on hand (let's say for a test), than the first way would be more effective.
4 0
3 years ago
there are 6 elementary schools in district. each school has 412 students. how many students in all are in the district? Solve th
kiruha [24]

Answer:

2472 students

Step-by-step explanation:

<u>What we know:</u>

- There are 6 schools

- Each school has 412 students

<u>What we're trying to solve:</u>

How many students are there altogether?

To find this, we multiply 412 by 6. Doing this is essentially the same as adding 412 to itself 6 times for each school there is in the district.

412 students × 6 schools

= 2472 students

Therefore, there are 2472 students in the district.

I hope this helps!

3 0
3 years ago
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