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DaniilM [7]
3 years ago
6

Here are some values of sequence Q. Write a recursive definition for the sequence.

Mathematics
1 answer:
Rashid [163]3 years ago
4 0

Answer: Q(n) = Q(n - 1) + 2.5

Step-by-step explanation:

We have 3 values of the sequence Q(n)

These values are:

Q(1) = 3

Q(3) = 8

Q(7) = 18

I would think that this is a geometric sequence.

Remember that the equation for the n-th term of a geometric sequence is:

A(n) = A(1)*r^(n-1)

where r is a constant, and A(1) is the first term of the sequence.

If we rewrite the terms that we know of Q(n) in this way we get:

Q(3) = Q(1)*r^(3 - 1) = 3*r^2 = 8

Q(7) = Q(1)*r^(7 - 1) = 3*r^6 = 18

Then we have two equations:

3*r^2 = 8

3*r^6 = 18

We should see if r is the same for both equations:

in the first one we get:

r^2 = 8/3

r = (8/3)^(1/2) = 1.63

and in the other equation we get:

r^6 = 18/3

r = (18/3)^(1/6) = 1.34

Then this is not a geometric sequence.

Now let's see if this is an arithmetic sequence.

The n-th term of an arithmetic sequence is written as:

A(n) = A(1) + (n - 1)*d

where d is a constant.

If we write the terms of Q(n) that we know in this way we get:

Q(3) = Q(1) + (3 - 1)*d = 3 + 2*d = 8

Q(7) = Q(1) + (7 - 1)*d = 3 + 6*d = 18

We need to see if d is the same value for both equations.

in the first one we get:

3 + 2*d = 8

2*d = 8 - 3 = 5

d = 5/2 = 2.5

In the second equation we get:

3 + 6*d = 18

6*d = 18 - 3 = 15

d = 15/6 = 2.5

d is the same for both terms, then this is an arithmetic sequence.

An arithmetic sequence is a sequence where the difference between any two consecutive terms is always the same value (d)

Then the recursive relation is written as:

A(n) = A(n - 1) + d

Then the recursive relation for Q is:

Q(n) = Q(n - 1) + 2.5

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Answer:

  (smallest, largest) = (B, C), (D, E), (G, J)

Step-by-step explanation:

Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

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<h3>ΔABC</h3>

The shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.

  • smallest angle: B
  • largest angle: C
<h3>ΔDEF</h3>

The shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.

  • smallest angle: D
  • largest angle: E
<h3>ΔGHJ</h3>

The shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.

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<em>Additional comment</em>

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2 years ago
Current Attempt in Progress
monitta

If at June 1, 2022, Sheffield Corp. had an Accounts Receivable balance of $ 18,900. During the month, the company had credit sales of $

24,500 and collected Accounts Receivable of $ 28,500. The balance in Accounts Receivable at June 30, 2022 will be: $14,900

Using this formula

2022 Balance in Accounts Receivable=Accounts Receivable balance as on June 1, 2022+ Credit sales  -Collected Accounts Receivable

Let plug in the formula

2022 Balance in Accounts Receivable=$18,900+$24,500-$28,500

2022 Balance in Accounts Receivable=$14,900

Inconclusion if at June 1, 2022, Sheffield Corp. had an Accounts Receivable balance of $ 18,900. During the month, the company had credit sales of $

24,500 and collected Accounts Receivable of $ 28,500. The balance in Accounts Receivable at June 30, 2022 will be: $14,900

Learn more here:

brainly.com/question/24297448

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96% answer.

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