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Oksi-84 [34.3K]
3 years ago
15

Enter a recursive rule for the geometric sequence. 6, −18, 54, −162, ...

Mathematics
1 answer:
svlad2 [7]3 years ago
5 0

Answer:

The required recursive formula is:

a_n=(-3)\times a_{n-1}

Step-by-step explanation:

We are given a geometric sequence as:

6,-18,54,-162,.....

Clearly after looking at different terms of the sequence we could observe that the sequence is an geometric progression (G.P.) with common ratio= -3 denoted by r.

Let a_n represents the nth term of the sequence.

This means that:

a_1=6, a_2=-18, a_3=54, a_4=-162,......

As the common ratio is -3.

so,

a_1=6\\\\a_2=-18=(-3)\times a_1\\\\a_3=54=(-3)\times a_2\\\\.\\.\\.\\.\\.\\.\\.\\.\\.a_n=(-3)\times a_{n-1}

Hence, the required recursive formula for the geometric sequence is:

a_n=(-3)\times a_{n-1}

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A purse contains $2.95 in quarters and dimes. The number of quarters exceeds the number of dimes by 2. Find the number of quarte
abruzzese [7]

Answer:

9 quarters and 7 dimes

Step-by-step explanation:

1 quarter = $0.25

1 dime = $0.10

9 (0.25) = $2.25

7 (0.10) = $0.70

2.25 + 0.70 = $2.95

4 0
3 years ago
For the function f(x)
WITCHER [35]

Given:

The function is

f(x)=\dfrac{8\sqrt[3]{x}-8}{9}

To find:

The inverse function f^{-1}(x).

Solution:

We have,

f(x)=\dfrac{8\sqrt[3]{x}-8}{9}

Step 1: Putting f(x)=y, we get

y=\dfrac{8\sqrt[3]{x}-8}{9}

Step 2: Interchange x and y.

x=\dfrac{8\sqrt[3]{y}-8}{9}

Step 3: Isolate variable y.

9x=8\sqrt[3]{y}-8

9x+8=8\sqrt[3]{y}

\dfrac{9x+8}{8}=\sqrt[3]{y}

Taking cube on both sides, we get

\left(\dfrac{9x+8}{8}\right)^3=y

y=\left(\dfrac{9x+8}{8}\right)^3

Step 4: Putting y=f^{-1}(x), we get

f^{-1}(x)=\left(\dfrac{9x+8}{8}\right)^3

Therefore, the correct option is C.

4 0
2 years ago
Solve using a2 + b2 = c2 <br> show ur work please :)
Brrunno [24]
So 90^2+90^2=c^2
8100+8100=c^2
16200=c^2
C= ~127.28
5 0
3 years ago
3(2+4x)=−7x2<br> please give step by step and end with improper fraction as answer
SVETLANKA909090 [29]

Answer:

\frac{-5}{3}

Step-by-step explanation:

3(2 + 4x) = -7 x 2  Distribute the 3

6 + 12x  = -14  Subtract 6 from both sides of the equation

12x = -20  Divide both sides by 12

x = \frac{-20}{12}  Divide the top and the bottom of the fraction by 4

x = \frac{-5}{3}

6 0
2 years ago
Read 2 more answers
I really help with this ill mark u brainliest pls
erma4kov [3.2K]

Answer:

m\angle XYW  = (155 - 20x)\degree

Step-by-step explanation:

m\angle XYZ= m\angle XYW +m\angle WYZ\\\\150\degree = m\angle XYW +(20x-5)\degree \\\\150\degree - (20x-5)\degree = m\angle XYW  \\\\(150 - 20x+5)\degree = m\angle XYW  \\\\(155 - 20x)\degree = m\angle XYW  \\\\m\angle XYW  = (155 - 20x)\degree \\\\

7 0
3 years ago
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