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My name is Ann [436]
2 years ago
14

What is the value of y in the sequence below? 2,y,18, -54,162,

Mathematics
1 answer:
snow_lady [41]2 years ago
7 0

First, let's check if the sequence is geometric or arithmetric.

If arithmetric, the sequence will have common difference.

<u>A</u><u>r</u><u>i</u><u>t</u><u>h</u><u>m</u><u>e</u><u>t</u><u>r</u><u>i</u><u>c</u>

\displaystyle \large{a_{n + 1} - a_n = d}

d stands for a common difference. Common Difference means that sequences must have same difference after subtracting.

<u>G</u><u>e</u><u>o</u><u>m</u><u>e</u><u>t</u><u>r</u><u>i</u><u>c</u>

\displaystyle \large{ \frac{a_{n + 1}}{a_n}  = r}

r stands for a common ratio.

To find the value of y, you can check the sequence. If we try subtracting the sequences, the differences are different. That means the sequences are not arithmetric. That only leaves the geometric sequence.

Let's check by dividing sequences.

We have:

  • 2,y,18,-54,162,...

Let's check by divide -54 by 18 and 162 by -54. We need to divide more than one so we can prove that the sequence is geometric.

\displaystyle \large{ \frac{ - 54}{18}  = - 3 } \\  \displaystyle \large{ \frac{ 162}{ - 54}  = - 3}

Hence, the sequence is geometric.

Because the common ratio is -3. Let these be the following:

\displaystyle \large{ a_{n + 1} = y } \\  \displaystyle \large{ a_n = 2 } \\  \displaystyle \large{ r =  - 3 }

From the:

\displaystyle \large{ \frac{a_{n + 1}}{a_n}  = r}

Substitute the values in.

\displaystyle \large{ \frac{y}{2}  =  - 3}

Multiply the whole equation by 2 to isolate y.

\displaystyle \large{ \frac{y}{2} \times 2  =  - 3 \times 2} \\  \displaystyle \large{ y =  - 6}

Therefore, the value of y is -6.

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<img src="https://tex.z-dn.net/?f=2m%20-%20%28m%20%2B%201%29%20%3D%200" id="TexFormula1" title="2m - (m + 1) = 0" alt="2m - (m +
natali 33 [55]

Answer: ..........................................................................................................................................................................................................................................................

8 0
3 years ago
Does anyone know the answer ? lmk asap
horrorfan [7]

Answer:

1,253 inches cubed

Step-by-step explanation:

This is easy, just find the separate volumes of both and add.

Figure 1: 7x5x5= 175 inches cubed

Figure 2: 11x14x7= 1,078 inches cubed

Added together: 1,253 inches cubed

Therefore it's C

:))))))

6 0
3 years ago
PLEASE HELP ASAP!!!
MAVERICK [17]

Answer:

y - 2, 3, 4, 5

Hope this helps :)

3 0
2 years ago
Needs help please :)
Degger [83]
the thing is I can't see it prop ley:(
8 0
3 years ago
Can someone help will give brainliest
Sonbull [250]

Answer:

Looking at this, slope seems to be 2 for the graph

So, looking at your options, -4 is less than 2, therefore, the answer is

D, with slope -4

6 0
2 years ago
Read 2 more answers
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