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alexandr1967 [171]
3 years ago
15

What is the sum of the geometric series 2+6+18+...+486?

Mathematics
1 answer:
marin [14]3 years ago
6 0

Answer:

728

Step-by-step explanation:

2+6+18+...+486

a=2

r=6/2=3

a_{n}=ar^{n-1}\\486=2(3)^{n-1}\\3^{n-1}=486/2=243=3^5\\n-1=5\\n=5+1=6\\S_{6}=2\frac{3^6-1}{3-1} \\=2\frac{729-1}{2}\\=728

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Answer:

The other endpoint of the​ segment is (-18,-7).

Step-by-step explanation:

The midpoint of the points (x_1,y_1) and (x_2,y_2) is given by the following formula:

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where (x_m,y_m) = coordinates of the midpoint.

We know that the midpoint is (-15, 2) and an endpoint is (-12, 11). Substituting the information we have gives:

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To find x_1 we need to solve this equation:

-15=\frac{x_1-12}{2} \\\\\frac{x_1-12}{2}=-15\\\\\frac{2\left(x_1-12\right)}{2}=2\left(-15\right)\\\\x_1-12=-30\\\\x_1-12+12=-30+12\\\\x_1=-18

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