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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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Step-by-step explanation:

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What is the factored form of the expression?<br><br> d^2 = 36d + 324
Veseljchak [2.6K]

Answer:

(x-43.45)(x+7.45)=0

Step-by-step explanation:

We have the quadratic equation d^{2}=36d+324  i.e. d^{2}-36d-324=0

As, the roots of the quadratic equation ax^{2}+bx+c=0 are given by x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}.

So, from the given equation, we have,

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Substituting the values in x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}, we get,

x=\frac{36\pm \sqrt{(-36)^{2}-4\times 1\times (-324)}}{2\times 1}

i.e. x=\frac{36\pm \sqrt{1296+1296}}{2}

i.e. x=\frac{36\pm \sqrt{2592}}{2}

i.e. x=\frac{36\pm 50.9}{2}

i.e. x=\frac{36+50.9}{2}  and x=\frac{36-50.9}{2}

i.e. x=\frac{86.9}{2}  and x=\frac{-14.9}{2}

i.e. x = 43.45 and x = -7.45

Thus, the roots of the equation are 43.45 and -7.45.

Hence, the factored form of the given expression will be (x-43.45)(x+7.45)=0

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Answer:

n=10

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6 = n-4

Add 4 to each side

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