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Luba_88 [7]
3 years ago
8

An arithmetic sequence "a" starts with 84, 77 define "a" recursively

Mathematics
1 answer:
sweet [91]3 years ago
4 0

Answer:

First, let's define an arithmetic sequence:

In an arithmetic sequence, the difference between any two consecutive terms is always the same.

Then we can write it in a general way as:

aₙ = a₁ + (n - 1)*d

where:

aₙ is the n-th term of the sequence.

d is the constant difference between two consecutive terms.

a₁ is the initial term of our sequence.

Now in this case we know that the first terms of our sequence are:

84, 77, ...

Then we know the initial term of our sequence:

a₁ = 84.

And the value of d can be calculated as:

d = a₂ - a₁ = 77 - 84 = -7

Then the general way of writing this sequence is:

aₙ = 84 + (n - 1)*(-7)

And the recursion relation is:

aₙ = aₙ₋₁ - 7

So for the n-th term, we must subtract 7 of the previous term.

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Michael Chan leaves a dock in his motorboat and travels at an average speed of 9 mph toward the Isle of Shoals, a small island o
horsena [70]

Since the motor boat left the dock 2 hours before the tour boat, their meeting point will be 27 miles from the dock from which both boats departed after 3 hours.

<h3>What is the distance?</h3>

Distance is the movement of an object regardless of direction. The distance can be defined as the amount of length an object has covered, regardless of its starting or ending position

We know that r × t = d

r = rate of speed

t = time

d = distance

For the motor boat

9 × t = d = rate × time

For the tour boat

27 × (t - 2) = d = rate × time

When they both cover the same distance in the same amount of time, they will eventually cross paths.

They both cover the same d-mile distance, so:

9 ×t = 27 × (t - 2)

Simplify to get:

9 × t = 27 × t - 54

18 t = 54

t = 3

The motor boat will have traveled at 9 mph for 3 hours to make a distance of 9 × 3 = 27 miles.

The tour boat will have traveled at 27 mph for 1 hour to make a distance of 1 × 27 = 27 miles.

Since the motor boat left the dock 2 hours before the tour boat, their meeting point will be 27 miles from the dock from which both boats departed after 3 hours.

To know more about distance visit: brainly.com/question/18850325

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8 0
2 years ago
A circle with a diameter of 25 inches
Oksana_A [137]

A =πr2

Π  = 3.14

r = ½diameter = 25/2 =12.5 inches

∴ Area = 3.14 × 12.5 × 12.5 square inches

  Area = 490.625 square inches

5 0
3 years ago
If n is a positive even number, then the product of (-12)ⁿ will be what
kipiarov [429]

Answer:

a positive even number.

Step-by-step explanation:

I suggest plugging in random positive even numbers and finding a pattern. (-12)^2 = 144. (-12)^ 4= 20,736. this is because two negatives, when multiplied, turn to a positive. the n is how many times negative 12 is multiplied with itself

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3 years ago
Write 800 as the product of its prime factors.
Alex_Xolod [135]
800|2
800|2
400|2
200|2
100|2
50|2
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5|5
1

800=2^5\cdot5^2


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3 years ago
What is greater 5.3 or 5.30
Simora [160]
5.30 because 3 is smaller than 30
7 0
3 years ago
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