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Softa [21]
3 years ago
12

In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if i

t exists, and if possible find the sixth term.
2a, 2a^(2)b, 2a^(3)b^(2), 2a^(4)b^(3). . .
Mathematics
2 answers:
bonufazy [111]3 years ago
5 0
This is a geometric sequence as each term is a constant ratio of the previous term, called the common ratio...

2a^2b/2a=(2a^3b^2)/(2a^2b)=ab and the first term is 2a

So the rule is:

a(n)=2a(ab)^(n-1)

a(6)=2a(ab)^5=2a^6(b^5)

We cannot know for sure if this series is infinite or not.  It would depend on what the values of a and b were.

If EITHER a^2 or b^2 is less than one the series would be finite (and technically a sequence and not a series),and a sum could be found.  If a^2 AND b^2 are greater than one it is an infinite series whos sum diverges....
Advocard [28]3 years ago
3 0
The sequence is infinite  because  the exponents   2 ,3 ,4 ,... go on infinitely.

That next number in the equence is obtained by multiplying each term by ab.

the sixth term is   2a^(6)b^(5)
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208

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Helen got a 7% reduction in the price of pair jeans that are normally $32. What is the approximate percent decrease in the price
Colt1911 [192]

A percentage is a way to describe a part of a whole. The approximate percent decrease in the price is 21.87%, thus, the correct option is B.

<h3>What are Percentages?</h3>

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given the reduction in the price is $7, while the original cost is $32. Therefore, the approximate percent decrease in the price is,

Percentage decrease = 7/32  × 100%

                                     = 21.87%

Hence, the approximate percent decrease in the price is 21.87%, thus, the correct option is B.

The correct question is:

Helen got a $7 reduction in the price of a pair of jeans that are normally $32. What is the approximate percent decrease in the price?

The percent decrease is approximately 15%.

The percent decrease is approximately 21%.

The percent decrease is approximately 43%.

The percent decrease is approximately 78%

Learn more about Percentages:

brainly.com/question/6972121

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3 0
2 years ago
if the recipe takes 60 minutes to cook at a temperature of 350 degrees how many minutes would it take at 200 degrees
Lady_Fox [76]

Answer:

34.28 minutes

Step-by-step explanation:

60:350=x:200

12000=350x

x=34.28

5 0
3 years ago
Read 2 more answers
If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyra
bearhunter [10]

Answer:

720 sq units.

Step-by-step explanation:

Length and width of square prism, w = 12 units

Height of square prism, x = 7 units

Height of square pyramid, y = 8 units

Please have a look at the attached image.

Here 2 Surfaces will not be exposed which are base of the square pyramid and the top of the square prism i.e. 2 square surfaces will not be exposed.

Here, surface area of the composite figure will be:

<em>Surface Area of Composite Figure = Lateral surface area of Square Pyramid + Surface Area of 5 surfaces of the square prism</em>

For finding the lateral surface area of pyramid, we need to find the slant height of the pyramid.

Let slant height be l units.

Using pythagoras theorem, we can find out the value of l.

As per theorem:

Hypotenuse^{2} = Base^{2} + Height^{2}\\

\Rightarrow l^{2} = (\dfrac{w}{2})^{2} + y^{2}\\\Rightarrow l^{2} = (\dfrac{12}{2})^{2} + 8^{2}\\\Rightarrow l^{2} = {6}^{2} + 8^{2}\\\Rightarrow l^{2} = 36+64 =  100\\\Rightarrow l = 10\ units

Lateral surface area of square prism = 4 \times Area of triangular surface

\Rightarrow 4 \times \dfrac{1}{2}\times Base \times Slant\ Height\\\Rightarrow 4 \times \dfrac{1}{2} \times 10 \times 12\\\Rightarrow 240\ sq\ units

Surface Area of 5 surfaces of the square prism =

4 \times x \times w + w^2\\\Rightarrow 4 \times 12 \times 7 + 12^2\\\Rightarrow 336 +144\\\Rightarrow 480\ sq\ units

So, total surface area of composite figure:

240 + 480 = 720 sq units.

7 0
3 years ago
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