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tresset_1 [31]
3 years ago
12

What are the steps to construct parallel lines using a compass and straightedge?

Mathematics
1 answer:
nevsk [136]3 years ago
4 0

See if the distance between the two lines is consistent with a compass.

Make sure the lines intersect at right angles with the corner of a piece of paper.

Measure each of the angles with a straightedge.

There is no way to ensure you have constructed parallel lines.

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What is the 7th term of the geometric sequence where a1 = -625 and a2 = 125
kykrilka [37]
Since the sequence is geometric, there is some constant r such that the sequence is recursively given by

a_n=ra_{n-1}

By this definition, you can recursively substitute into the right hand side the definition for a_{n-1},a_{n-2},\ldots to find an explicit formula for the nth term.

a_n=ra_{n-1}=r^2a_{n-2}=r^3a_{n-3}=\cdots=r^{n-1}a_1=-625r^{n-1}

You know the second term, which means you can find r:

a_2=-625r^{2-1}\implies125=-625r\implies r=-\dfrac15

So, the 7th term of the sequence is

a_7=-625\left(-\dfrac15\right)^{7-1}=-\dfrac1{25}
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