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grandymaker [24]
2 years ago
13

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 4, 2, 1

, ...
I need the help now ​
Mathematics
1 answer:
BigorU [14]2 years ago
5 0

Answer:

geometric with r = \frac{1}{2}

Step-by-step explanation:

An arithmetic sequence has a common difference (d) between consecutive terms

2 - 4 = - 2

1 - 2 = - 1

Then d is not common , not an arithmetic sequence

A geometric sequence has a common ratio (r ) between consecutive terms

2 ÷ 4 = 0.5

1 ÷ 2 = 0.5

Then common ratio r = \frac{1}{2}

Thus sequence is geometric

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A container in the shape of this cuboid holds 2 litres of water.
zysi [14]

Given:

Volume of cuboid container = 2 litres

The container has a square base.

Its height is double the length of each edge on its base.

To find:

The height of the container.

Solution:

We know that,

1 litre = 1000 cubic cm

2 litre = 2000 cubic cm

Let x be the length of each edge on its base. Then the height of the container is:

h=2x

The volume of a cuboid is:

V=l\times w\times h

Where, l is length, w is width and h is height.

Putting V=2000,\ l=x,\ w=x,\ h=2x, we get

2000=x\times x\times 2x

2000=2x^3

Divide both sides by 2.

1000=x^3

Taking cube root on both sides.

\sqrt[3]{1000}=x

10=x

Now, the height of the container is:

h=2x

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Therefore, the height of the container is 20 cm.

8 0
3 years ago
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
lubasha [3.4K]

Answer:

The answer is option C.

<h3>-6, -5 2/5, -4 1/5</h3>

Step-by-step explanation:

The arithmetic sequence is given by

A(n) =  - 6 + (n - 1)( \frac{1}{5} )

where n is the number of terms

<u>For</u><u> </u><u>the</u><u> first</u><u> </u><u>term</u>

n = 1

So we have

A(1) =  - 6 + (1 - 1)( \frac{1}{5} )

=  - 6 + (0)( \frac{1}{5} )

=  - 6

<u>For</u><u> </u><u>the</u><u> </u><u>fou</u><u>rth</u><u> term</u>

n = 4

A(4) =  - 6 + (4 - 1)( \frac{1}{5} )

=  - 6 + (3)( \frac{1}{5} )

=  - 5 \frac{2}{5}

<u>For</u><u> </u><u>the</u><u> </u><u>tenth</u><u> </u><u>term</u>

n = 10

A(10) =  - 6 + (10 - 1)( \frac{1}{5} )

=  - 6 + (9)( \frac{1}{5} )

=  - 4 \frac{1}{5}

Hope this helps you

4 0
2 years ago
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