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Andrej [43]
1 year ago
8

Find the 21st term in the arithmetic sequence. 3, 7, 11, 15, 19, ...

Mathematics
1 answer:
NNADVOKAT [17]1 year ago
5 0

The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.

<h3>What is the nth term of an arithmetic series?</h3>

The nth term of an arithmetic sequence is calculated by the formula

aₙ = a + (n - 1) · d

Here the first term is 'a' and the common difference is 'd'.

<h3>Calculation:</h3>

The given sequence is an arithmetic sequence.

3, 7, 11, 15, 19, ....

So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.

Thus, the required 21st term in the sequence is

a₂₁ = 3 + (21 - 1) × 4

⇒ a₂₁ = 3 + 20 × 4

⇒ a₂₁  = 3 + 80

∴ a₂₁  = 83

So, the 21st term in the given arithmetic sequence is 83.

Learn more about the arithmetic sequence here:

brainly.com/question/6561461

#SPJ1

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A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to
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Answer:

20%

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3 years ago
URGENT! PLEASE HELP.
Harrizon [31]

The distance BC from Tower 2 to the plane will be 14,065.5 ft and the height of the plane from the ground will be 5,720.9 ft.

<h3>What is a right-angle triangle?</h3>

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

A plane is located at C on the diagram.

There are two towers located at A and B.

The distance between the towers is 7600 feet and angles of elevation are given.

Then in the right-angle triangle ΔADC, we have

\rm \tan 16 = \dfrac{H}{7600 + X}\\\\\\H = 0.2867(7600 +X)\\\\\\H = 0.2756\ X + 2179.2649 ...1

Then in the right-angle triangle ΔBDC, we have

\rm \tan24 = \dfrac{H}{ X}\\\\\\H = 0.4452\ X ...2

From equations 1 and 2, we have

0.4452X = 0.2756 X + 2179.2649

0.1696X = 2179.2649

            X = 12849.439 ≅ 12,849.4 ft

Then the distance BC from Tower 2 to the plane will be

\rm BC = \dfrac{12849.4}{\cos 24}\\\\\\BC = 14065.5 \ ft

Then the height of the plane from the ground will be

\rm H = 12849.4 \times  \tan 24 \\\\\\H = 5720.9 \ ft

The figure is shown below.

More about the right-angle triangle link is given below.

brainly.com/question/3770177

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2 years ago
Name the property of real numbers illustrated by the equation 2*(√8*7)=(2*√8)*7
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Associative property of mulipication, the ability to move parenthasees with mltipication or additon
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3 years ago
Read 2 more answers
Why would |3-6| be 3 instead of -3?
Delicious77 [7]
Because you can have a negative inside the absolute value so even if it is inside the absolute value of -3 will come out as 3.
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3 years ago
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