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2 years ago

What is the sum of the first 5 terms of this geometric series? Use . -4 + 12 + (-36) + ⋯

Mathematics

1 answer:

yKpoI14uk [10]2 years ago

7 0

Answer:

The sum of the first 5 terms is -244

Step-by-step explanation:

To calculate the sum of the geometric series, we need the first term, the common ratio and the number of terms we would like to sum.

The first term here is -4

The common ratio is T2/T1 or T3/T2 = 12/-4 = -3

number of terms n = 5

The formula to use is;

Sn = a(1-r^n)/(1-r)

Plugging these values, we have;

Sn = -4(1-(-3)^5)/(1-(-3))

Sn = -4(1+243)/4 = -1(244) = -244

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For this case we have:

Question 1:

According to Heron's formula, the area of a triangle is given by:

$A=\sqrt{(s(s-a)(s-b)(s-c))}$

Where a, b and c are the sides of the triangle and s is the semi-perimeter of the triangle given by:

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Let:

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We have s:

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Substituting in the formula of the area:

$A=\sqrt{(35(35-20)(35-23)(35-27))}\\A=\sqrt{(35(15)(12)(8))}\\A=\sqrt{(50400)}\\A=224.5mm^2$

Thus, the area of the triangle is $A = 224.5mm ^ 2$

Answer:

$A = 224.5mm ^ 2$

Question 2:

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Where:

b: Base of the triangle

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Let:

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Where:

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So:

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Substituting:

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Thus, the area of Laura's carpet is given by $A = 72 feet ^ 2$

Answer:

$A = 72 feet ^ 2$

Question 4:

We must take out the area of the outer wall, given by a rectangle, then:

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Where:

l: It is the length of the rectangle

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A regular hexagon is formed by 6 equal triangles. The area of the hexagon is given by:

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Thus, the area of the hexagon is $A = 150cm ^ 2$

Answer:

$A = 150cm ^ 2$

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