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2 years ago

Given the explicit formula an=3(-4)n-1, what is the sixth term?

Mathematics

1 answer:

Sholpan [36]2 years ago

5 0

Answer:

a6 = -3072

Step-by-step explanation:

Put 6 where n is and do the arithmetic.

Since the form of your function looks like it is trying to describe a geometric sequence, we assume you actually mean ...

an = 3(-4)^(n-1)

So, for n=6, this has the value ...

a6 = 3(-4)^(6-1) = 3(-1024)

a6 = -3072

_____

Same deal if you really mean

an = -12n -1

a6 = -12(6) -1 = -73

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Calculate the perimeter of a square with side length of 9 cm don not include units in your answer

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Answer: 36

Step-by-step explanation:

Each side of square are equal length

4 sides

9+9+9+9=36

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3 years ago

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Step-by-step explanation:

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3 years ago

Describe and correct the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28.

ycow [4]

Answer: The tenth term is 76

=======================================================

Explanation:

We use this arithmetic sequence formula to get the nth term

$a_n = a_1 + d(n-1)$

Plug in $a_1 = 4, \ d = 8, \ n = 10$ and you should get the following:

$a_n = a_1 + d(n-1)\\\\a_{10} = 4 + 8(10-1)\\\\a_{10} = 4 + 8(9)\\\\a_{10} = \textbf{76}\\\\$

The tenth term is <u>76</u>

---------

We can verify this by listing out the terms one by one. Start at 4, add on 8 each time, until you generate the 10th term. A table like the one shown below is a good way to keep track of all the terms.

$\begin{array}{c|c}\boldsymbol{n} & \boldsymbol{a_n}\\1 & 4\\2 & 12\\3 & 20\\4 & 28\\5 & 36\\6 & 44\\7 & 52\\8 & 60\\9 & 68\\10 & \textbf{76}\\\end{array}$

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In short, the error is with the "10" in the expression 4+10(8). The student should have used 9 instead. This is because of the n-1 term in $a_n = a_1 + d(n-1)$ which shifts everything one spot to the left.

7 0

2 years ago

Al producir q artículos, el precio es p=32-q y el costo total esta dado por C=80+8q. Determine la función de utilidad que depend

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3 years ago

A house was valued at $100,000 in the year 1987. The value appreciated to $165,000 by the year 2002.

iris [78.8K]

Answer:

A) The annual multiplier was 1.0339; the annual increase was 0.0339 of the value.

B) 3.39% per year

C) $182,000

Step-by-step explanation:

A) Let's let t represent years since 1987. Then we can fill in the numbers and solve for r.

165000 = 100000(1 +r)^15

1.65^(1/15) = 1 +r . . . . . divide by 100,000; take the 15th root

1.03394855265 -1 = r ≈ 0.0339

The value was multiplied by about 1.0339 each year.

B) The value increased by about 3.39% per year.

C) S = $100,000(1.03394855265)^18 ≈ $182,000

8 0

3 years ago