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charle [14.2K]
3 years ago
8

Determine the nth term for each of the following sequences:16,15,14,13,12,..

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0
F(n) = 1st term - common difference (n - 1)

The operation is subtraction because the sequence is decreasing.

n = number of the term you are looking for
1st term = 1st number in the sequence, in this case, 16
common difference = difference between one number to the next

f(n) = 16 - 1(n-1)

Assuming we are looking for the 5th term.
f(5) = 16 - 1(5-1)
       = 16 - 1(4)
       = 16 - 4
       = 12     * as you can see, 12 is the 5th term of the sequence.

If you are looking for the equivalent of the nth term, simply substitute n by the number you are looking for and solve the equation.
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What is the recursive rule for this geometric sequence? 27,  9,  3,  1,  ... Enter your answers in the boxes.
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Answer:

a_n=a_{n-1}(\frac{1}{3})\\a_1=27

Step-by-step explanation:

A recursive formula is a formula in which each term is based on the previous term.

In a geometric sequence, each term is found by multiplying the previous term by a constant.

To get from 27 to 9, then from 9 to 3, etc., we would multiply by 1/3.  This makes the common ratio 1/3.

The recursive formula for a geometric sequence is

a_n=a_{n-1}(r), where a_n represents the general term,  a_{n-1}, represents the previous term, and r represents the common ratio.

Plugging in our values, we have

a_n=a_{n-1}(r)

We also have to indicate what the first term, a₁, is.  In this sequence, it is 21.  This gives us

a_n=a_{n-1}(\frac{1}{3})\\a_1=27

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if (1,-7) is in the solution area of the inequality y ≤ 1x + b, what is the smallest value of b possible?
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3 years ago
Jake built a skateboard ramp, if the distance of the ramp is 10 ft. The ramp rises a
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Answer:

Angle made by ramp with ground is ≈19.29^{\circ}

Step-by-step explanation:

Diagram of given scenario is shown below.

Given that,

Horizontal Distance of Skateboard ramp is 10 ft.

Height of Skateboard ramp is 3.5 ft.

From figure,

It is forming a Right angle triangle \triangle ABC.

In \triangle ABC, AB=3.5 and BC=10.

Clearly see that we need to find measure of angle \angle C.

Using Trigonometric ratio:

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So,  Tan(\angle C) = \frac{AB}{BC} =\frac{3.5}{10} =0.35

Then \angle C=Tan^{-1} (3.5)=19.290046^{\circ}

Therefore, Angle made by ramp with ground is ≈19.29^{\circ}

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