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2 years ago

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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If you make $8 an hour and you get a 10% raise how much are you making now

alexira [117]

Answer:

$8.8

Step-by-step explanation:

$8*0.10=0.8$

$8+0.8=8.8$

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3 years ago

Consider the cylinder with a volume of 132π cm3. A cylinder with volume of 132 pi centimeters cubed. What is the volume of a con

vagabundo [1.1K]

Answer:

44 pi centimeters cubed

Step-by-step explanation:

Since, base radius and height of cone are equal to to that of cylinder. Hence,

$Volume \: of \: cone \\ = \frac{1}{3} \times Volume \: of \: cylinder \\ = \frac{1}{3} \times132\pi \\ = 44\pi \: {cm}^{3}$

4 0

3 years ago

Read 2 more answers

Let U={x: x is an integer and 2≤x≤10}. In each of the following cases, find A,B and determine whether A⊆B,B⊆A, both or neither:

12345 [234]

A is not a subset of B but B is a subset of A (that is can be found in A) that is B⊆A is correct

<h3>Set theory</h3>

Set is defined as the arrangement of elements. They can be represented using the venn diagram.

Given the following sets

U = {x: x is an integer and 2≤x≤10} = {3, 4, 5, 6, 7, 8, 9}
A = {x: 2x+1>7} = {x > 3}

B={x: x^2>20} = {x >± 20}

From the set, can see that A is not a subset of B but B is a subset of A (that is can be found in A) that is B⊆A is correct

Learn more on sets here: brainly.com/question/13458417

8 0

2 years ago

Write the equation of the line that is perpendicular to y=2x-7 and passes through the point (6, 5)

Pani-rosa [81]

Answer:

Step-by-step explanation:

we are given a equation of a line

we want to figure out the equation of the perpendicular line passes through the <u>(</u><u>6</u><u>,</u><u>5</u><u>)</u><u> </u>points

in order to do so

recall that,

$\displaystyle m_{ \text{perpendicular}} = - \frac{1}{m}$

we got from our given equation that m=2

because equation of a line is y=mx+b

thus

$\displaystyle m_{ \text{perpendicular}} = - \frac{1}{2}$

remember that, when we want to figure out perpendicular line or parallel line we should the formula given by

$\displaystyle y - y_{1} = m(x - x_{1})$

since we got our perpendicular m is -½, $x_1=6$ and $y_1=5$ , substitute

$\displaystyle y - 5 = - \frac{1}{2} (x - 6)$

to get the perpendicular equation you should simplify the above equation to y=mx+b form

distribute -½:

$\displaystyle y - 5 = - \frac{1}{2} x + 3$

add 5 to both sides:

$\displaystyle y = - \frac{1}{2} x + 8$

hence,

our answer choice is B

3 0

3 years ago

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The area of the Pacific Ocean is about 6.0061 x 107 square miles. The area of the Southern Ocean is about 7.8483 x 106 square mi

Scilla [17]

Answer:

A. 8

Step-by-step explanation:

6.0061 x 10^7

/ = 6/8 x 10^7/10^6

7.8483 x 10^6

0.75 x 10^7-6

0.75 x 10^1

A: 0.75 = 7.5 = 8.

5 0

3 years ago