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notsponge [240]
4 years ago
10

Determine whether the sequence below is arithmetic or geometric, and find the function that will produce any given term in the s

equence: 16, 24, 36, 54, 81,
Is this sequence arithmetic?
Is this sequence Geometric?
What is the analytical representation of the sequence?
Mathematics
1 answer:
kondor19780726 [428]4 years ago
4 0

Answer:

Geometric Sequence.

nth term = an = 16(1.5^(n-1).  

Step-by-step explanation:

24/16 = 1.5

36/24 = 1.5

54/36 = 1.5

81/54 = 1.5

There is a common ratio between the terms so it is Geometric.

The nth term an = a1r^(n-1)   where a1 = first term , r = common ratio.

So here we have an = 16(1.5)^(n-1).

You might be interested in
A cereal company is exploring new cylinder-shaped containers. Two possible containers are shown in the diagram.x is 6 and r=4.5
KatRina [158]

Answer:

Container \rm X will have less label area than container \rm Y by about 9\; \rm in.

Step-by-step explanation:

A rectangular sheet of paper can be rolled into a cylinder. Conversely, the lateral surface of a cylinder can be unrolled into a rectangle- without changing the area of that surface.

Indeed, the width of that rectangle will be the same as the height of the cylinder. On the other hand, the length of that rectangle should be exactly equal to the circumference of the circles on the top and the bottom of the cylinder. In other words, if a cylinder has a height of h and a radius of r at the top and the bottom, then its lateral surface can be unrolled into a rectangle of width h and length 2\,\pi\, r.

Apply this reasoning to both cylinder \mathrm{X} and \rm Y:

For cylinder \mathrm{X}, h = 6\; \rm in while r = 4.5\; \rm in. Therefore, when the lateral side of this cylinder is unrolled:

  • The width of the rectangle will be 6\; \rm in, while
  • The length of the rectangle will be 2 \, \pi \times 4.5\; \rm in = 9\, \pi\; \rm in.

That corresponds to a lateral surface area of 54\, \pi\; \rm in^2.

For cylinder \rm Y, h = 10.5\; \rm in while r = 3\; \rm in. Similarly, when the lateral side of this cylinder is unrolled:

  • The width of the rectangle will be 10.5\; \rm in, while
  • The length of the rectangle will be 2\pi\times 3\; \rm in = 6\,\pi \; \rm in.

That corresponds to a lateral surface area of 63\,\pi \; \rm in^2.

Therefore, the lateral surface area of cylinder \rm X is smaller than that of cylinder \rm Y by 9\,\pi\; \rm in^2.

5 0
3 years ago
Tell whether the sequence is arithmetic. If it is, identify the common difference. 4, 8, 16, 32, …
zaharov [31]

Answer:

it's geometric

8/4=2 16/8=2

d=2

5 0
3 years ago
(WILL MARK BRAINLIST)
mezya [45]
I believe the answer is the second one
4 0
2 years ago
One canned juice drink is 15% orange juice another is 10% orange juice how many liters of each should be mixed together in order
vfiekz [6]
\bf \begin{array}{lccclll}
&quantity(L)&concentration&
\begin{array}{llll}
concentrated\\
quantity
\end{array}\\
&-----&-------&-------\\
\textit{15\% juice}&x&0.15&0.15x\\
\textit{10\% juice}&y&0.10&0.10y\\
-----&-----&-----&-----\\
mixture&5&0.14&(5)(0.14)
\end{array}

whatever the amounts of "x" and "y" are, they must add up to 5Liters
thus x + y = 5

and whatever the concentrated quantity is in each, they must add up to (5)(0.14)

notice, that we use the decimal notation for the amount of juice concentration, that is, 15% is just 15/100 or 0.15, and 14% is just 14/100 or 0.14 and so on, recall that "whatever% of something" is just (whatever/100)*something

thus    \bf \begin{cases}
x+y=5\implies \boxed{y}=5-x\\\\
0.15x+0.10y=(5)(0.14)\\
----------\\
0.15x+0.10\left(\boxed{5-x}  \right)=(5)(0.14)
\end{cases}

solve for "x", to see how much of the 15% juice will be needed

what about "y"?  well, y = 5 - x

7 0
3 years ago
LITTERLY HELP ME PLEASEE..... 2/x-4x/2x-3=-2<br> PLEASEE I INSERTED A PIC
Stels [109]

Answer:

x = -3

Step-by-step explanation:

Given expression is,

\frac{2}{x}- \frac{4x}{2x-3}=-2

\frac{2(2x-3)}{x(2x-3)}-\frac{4x(x)}{x(2x-3)}=-2

\frac{2(2x-3)-4x^{2} }{x(2x-3)}=-2

(4x - 6) - 4x² = -2x(2x - 3)

4x - 6 - 4x² = -4x² + 6x

4x - 6 = 6x

6x - 4x = -6

2x = -6

x = -3

3 0
3 years ago
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