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Mice21 [21]
2 years ago
7

What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 3?

Mathematics
2 answers:
meriva2 years ago
3 0
Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

In this case a=5, and d=-2 so

a(n)=5-2(n-1)  which can be simplified...

a(n)=5-2n+2

a(n)=7-2n

The domain is restricted to integers from 1 to +oo.
sveticcg [70]2 years ago
3 0

Answer:

  1. a_n=7-2n
  2. All positive integers greater than 1 will be its domain.

Step-by-step explanation:

The explicit equation for an arithmetic sequence is,

a_n=a_1+(n-1)d

Where,

a_n = nth term in the arithmetic sequence,

a_1 = 1st term in the arithmetic sequence,

d = common difference.

Here, the first term of 5 and a second term of 3. So the common difference is -2.

Putting the values,

a_n=5+(n-1)(-2)=5+2-2n

i.e a_n=7-2n

As n neither be negative nor fraction, because it is the number of term, so all positive integers greater than 1 will be its domain.

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A circle with center at (12,−1) passes through (0,−1). Find the circumference and area of the circle in terms of p.
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Answer:

C = 75.36

A = 452.16

Step-by-step explanation:

Find the radius r by finding the distance between (12,-1) and (0,-1) using the distance formula.

d = \sqrt{(12-0)^2 + (-1--1)^2} =\sqrt{(12)^2 + (0^2} =\sqrt{144+0} =\sqrt{144}=12

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So the circumference of the circle is C = 2\pi r = 2\pi 12 = 24\pi = 75.36

So the area of the circle is A = \pi r^2\\A = \pi 12^2\\A = 144\pi\\A = 452.16

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