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velikii [3]
3 years ago
14

Find an explicit rule for the nth term of the sequence.

Mathematics
1 answer:
nlexa [21]3 years ago
8 0

Answer:

An explicit rule for the nth term of the sequence will be:

a_n=-4\cdot \:2^{n-1}      

Thus, option (A) is true.

Step-by-step explanation:

Given the sequence

-4, -8, -16, -32, ...

A geometric sequence has a constant ratio r and is defined by

a_n=a_0\cdot r^{n-1}

Computing the ratios of all the adjacent terms

\frac{-8}{-4}=2,\:\quad \frac{-16}{-8}=2,\:\quad \frac{-32}{-16}=2

As the ratio 'r' is the same.

so

r=2

as

a_1=-4

Hence, the nth term of the sequence will be:

a_n=a_0\cdot r^{n-1}

substituting the values r=2 and a_1=-4

a_n=-4\cdot \:2^{n-1}      

Therefore, an explicit rule for the nth term of the sequence will be:

a_n=-4\cdot \:2^{n-1}      

Thus, option (A) is true.

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DC = \sqrt{(7 - 7)^{2} + (4 - (-1))^{2} }

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Now, find the distance between AB and BC

AB = \sqrt{(-2 - 2)^{2}  + (-5 - 4)^{2} }

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⇒ AB = \sqrt{16 + 81}

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Hence, AB = BC = √97

In the given quadrilateral, the two pair is of equal length and these sides are adjacent to each other.

Hence, it follows the property of kite.

For more questions on quadrilateral, visit:

brainly.com/question/23935806

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1 year ago
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Answer:

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We are being asked for times, so we can express the rate in terms of seconds per meter.

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As you plot both equations on the same graph, you will get something like this, shown in the graph.

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Answer:

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