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SCORPION-xisa [38]
3 years ago
15

What is the sum of the first seven terms of the geometric series 2 - 10 +50 -...?

Mathematics
1 answer:
Umnica [9.8K]3 years ago
3 0

Answer:

26042.

Step-by-step explanation:

What's the first term of this geometric series?

2.

What's the common ratio of this geometric series?

Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2.

\displaystyle r = \frac{-10}{2} = -5.

What's the sum of this series to the seventh term?

The sum of the first n terms of a geometric series is:

\displaystyle a_1 \cdot \frac{1-r^{n}}{1-r},

where

  • a_1 is the first term of the series,
  • r is the common ratio of the series, and
  • n is the number of terms in this series.

\displaystyle 2 \times\frac{1- (-5)^{7}}{1- (-5)}=26,042.

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Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)
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Answer:

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Step-by-step explanation:

A parabola with vertex at point C(x, y) = (h,k) and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

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y - Independent variable.

x - Dependent variable.

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h, k - Coordinates of the vertex.

The coordinates of the focus are represented by:

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The <em>latus rectum</em> is a line segment parallel to the x-axis which contains the focus. If we know that h = 2, k = -2 and p = -5, then the latus rectum is between the following endpoints:

By (2):

F(x,y) = (2, -2-5)

F(x,y) = (2,-7)

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There are two solutions:

x_{1} = 2 + 10

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x_{2} = 2-10

x_{2} = -8

Hence, the endpoints of the latus rectum are (12, -7) and (-8, -7).

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