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Agata [3.3K]
3 years ago
12

What expression shows the relationship between the value of any term and n, its position in the sequence for the given sequence?

-5, -8, -11, -14, -17, ...
Mathematics
1 answer:
xxTIMURxx [149]3 years ago
3 0
Ok, so it adds -3 each time

first term is -5

an=a1+d(n-1)
a1=first term
d=common difference

given
firs term=-5=a1
common difference=-3=d

an=-5-3(n-1) or
an=-5-3n+3=-2-3n 
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All integers where n ≥ 1.

We have given that the sequence,

a_{n} =4-3(n-1)

We have to find the domain for n.

<h3>What is the meaning of arithmetic sequence?</h3>

Arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Difference here means the second minus the first.

That is, a_{n} =a+(n-1)d

where a = first term of sequence.

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n =number of terms which belongs to natural numbers

By  the definition of arithmetic sequence n starts with 1

Remember that,the natural number starts with 1

Now, in given sequence  for nth term

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The domain for n is All integers where n ≥ 1.

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2 years ago
A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 9 cm. Find the volume of th
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The volume is the total space occupied by an object.

The volume of a sphere of radius r units is given as (4/3)πr³.

The volume of a cylinder with radius r units and height h units is given as πr²h.

In the question, we are asked to find the volume of the remaining solid when a sphere of radius 9cm is drilled by a cylindrical driller of radius 5cm.

The volume will be equal to the difference in the volumes of the sphere and cylinder, where the height of the cylinder will be taken as the diameter of the sphere (two times radius = 2*9 = 18) as it is drilled through the center.

Therefore, the volume of the ring-shaped remaining solid is given as,

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Answer:

2.8828283e+16

Step-by-step explanation:

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The reflection point P' would be (-6, 8)
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What transformation is shown below?
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