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3 years ago

Find a general term an for the sequence whose first four terms are given. 2, 4, 8, 16, ...

Mathematics

1 answer:

lapo4ka [179]3 years ago

7 0

Answer:

an = 2·2^(n-1)

Step-by-step explanation:

There are simple tests to determine whether a sequence is arithmetic or geometric. The test for an arithmetic sequence is to check to see if the differences between terms are the same. Here the differences are 2, 4, 8, so are not the same.

The test for a geometric sequence is to check to see if the ratios of terms are the same. Here, the ratios are ...

4/2 = 2

8/4 = 2

16/8 = 2

These ratios are all the same (they are "common"), so the sequence is geometric.

The general term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

Filling in the values for this sequence, we find the general term to be ...

an = 2·2^(n-1)

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Given, the distance around the edge of the table top is 4.7 ft.

That means the circumference given is 4.7 ft.

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Where, C = circumference, r = radius.

Here to get the area first we will find the radius of it. So we will substitute the value of circumference in the formula. We will get,

$4.7 = 2\pi r$

To get r, we will move $2\pi$ to the left side by dividing it to both sides. We will get,

$\frac{4.7}{(2\pi) } = \frac{(2\pi r )}{(2\pi) }$

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So we have got the radius here. Radius is 0.748 ft. We will have to find the area now. We know that the formula to find the area is,

$A = \pi r^2$ , where A = area, r = radius.

By substituting the value of r we will get,

$A = \pi (0.748)^2$

$A = 1.76$ (Approximately taken upto two decimal place)

So the area Nami needed = 1.76 square ft.

We have got the required answer here.

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Step-by-step explanation:

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