First, let's check if the sequence is geometric or arithmetric.
If arithmetric, the sequence will have common difference.
Arithmetric
[tex] \displaystyle \large{a_{n + 1} - a_n = d}[/tex]
d stands for a common difference. Common Difference means that sequences must have same difference after subtracting.
Geometric
[tex] \displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}[/tex]
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.
[tex] \displaystyle \large{ \frac{ - 54}{18} = - 3 } \\ \displaystyle \large{ \frac{ 162}{ - 54} = - 3} [/tex]
Hence, the sequence is geometric.
Because the common ratio is -3. Let these be the following:
[tex] \displaystyle \large{ a_{n + 1} = y } \\ \displaystyle \large{ a_n = 2 } \\ \displaystyle \large{ r = - 3 }[/tex]
From the:
[tex] \displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}[/tex]
Substitute the values in.
[tex] \displaystyle \large{ \frac{y}{2} = - 3}[/tex]
Multiply the whole equation by 2 to isolate y.
[tex] \displaystyle \large{ \frac{y}{2} \times 2 = - 3 \times 2} \\ \displaystyle \large{ y = - 6}[/tex]
Therefore, the value of y is -6.
Simplify the expression to determine the cost of the groceries 5.25+14.75+3.99 +2.01
Answer:
Cost of the groceries is 26.
Step-by-step explanation:
The expression is,
[tex]5.25+14.75+3.99+2.01[/tex]
Add the first two numbers,
[tex]5.25+14.75=20.[/tex]
Add the last two numbers,
[tex]3.99+2.01=6.[/tex]
Then, add the two answers,
[tex]20+6=26.[/tex]
That is,
[tex]5.25+14.75+3.99+2.01=26.[/tex]
S, the cost of the groceries is [tex]26.[/tex]
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Is 2.200929 rational
A sequence has the recursive definition of f(1)=2/3, f(n)=f(n-1)×3/2 for n≥2
Right the first five terms of the sequence
Leave answers as fractions
Answer:
Step-by-step explanation:
[tex]f(1)=2/3\\f(2)=f(1)\times (3/2)=(2/3)\times(3/2)=1\\f(3)=f(2)\times (3/2) = 1\times (3/2) = 3/2\\f(4)=f(3)\times (3/2) = (3/2)\times (3/2) = 9/4\\f(5)=(f(4)\times (3/2) = (9/4)\times (3/2) = 27/8[/tex]
So the first five terms are 2/3, 1, 3/2, 9/4, 27/8.
The first five terms are 2/3, 1, 3/2, 9/4, and 27/8 if the f(1)=2/3, and f(n) = f(n -1)×(3/2); for n ≥ 2.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that:
f(1)=2/3,
f(n) = f(n -1)×(3/2); for n ≥ 2
Plug n = 2
f(2) = f(2 -1)×(3/2)
f(2) = f(1)×(3/2)
f(2) = (2/3)(3/2)
f(2) = 1
Similarly;
f(3) = 3/2
f(4) = 94/
f(5) = 27/8
The first five terms are 2/3, 1, 3/2, 9/4, and 27/8.
Thus, the first five terms are 2/3, 1, 3/2, 9/4, and 27/8 if the f(1)=2/3, and f(n) = f(n -1)×(3/2); for n ≥ 2.
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please help me im being timed
Find the inverse of the function:
f(x)=−4x+8
Answer:
(x) = -x/4+2
Step-by-step explanation:
Inverse the function, so swap the places of x and y
x = -4y + 8
Then solve for y
x - 8 = -4y
-x/4 + 2 = y
y = -x/4 + 2
g(x) = -x/4+2
You are working with cable that has a loss rate of 5 dB per 100 ft. If you don’t want to lose more than 15 dB, what is the maximum number of feet of cable you can run
The maximum number of feet of cable that can be run is 300 feet.
An equation is an expression that is used to show the relationship between two or more variables and numbers.
Given a loss rate of 5 dB per 100 ft. Hence for a loss of less than 15dB:
Maximum length of cable = 15 dB / ( 5 dB per 100 ft.) = 300 feet.
The maximum number of feet of cable that can be run is 300 feet.
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hi please help i’ll give brain
Answer:
10
Step-by-step explanation:
Common factors of 110: 1, 2, 5, 10, 11, 22, 55, 110
Common factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 120.
The common factor of 110, 40, and 120 is 10.
[tex]f(x)=x^{4} -x^{3} -7x^{2} +10+5x[/tex]
1. write in standard form
2. use Descartes rule of sign
3. possible roots
4. first synthetic division
5. reconsider possible roots
6. second synthetic division
7. quadratic equation
8. solution set
Question in image, please help
Answer:
34 degrees
Step-by-step explanation:
the verical angle theorem says any two angles opposite of each other from intersecting lines have the same angle
Plz Help!!!!!!
At Suzie’s garden you can exchange vegetables and fruits instead of spending money. If you can exchange 6 cantaloupes for 12 tomatoes, 10 tomatoes for 20 grapes, and 18 grapes for 27 raspberries, how many raspberries could be exchanged for 20 cantaloupes?
Answer: 20 Cantaloupes will fetch 120 Raspberries.
Step-by-step explanation:
C = Cantaloupes
T = Tomatoes
G = Grapes
R = Raspberries
Conversions (exchange rates):
2T/C
2 G/T
1.5 R/G
Start with 20C
20C*(2T/C) = 40T
40T*(2 G/T) = 80G
80G*(1.5 R/G) = 120R
Solve 4 [5 (12+3)-2]-7 PLSSS HELP MEEE
Answer:
285
Step-by-step explanation:
4(5x15-2)-7
4(75-2)-7
4x73-7
292-7
285
Is the following statement true or false?
The intersection of two planes carl be a point.
true
false
Submit
False.
It could be a plane, a line, or no intersection at all. But it can't be a point.
Name 3 planes parallel to FL
Answer:
I have answered. it is perfect answer
Which point represents the opposite of -2?
Answer:
2
Step-by-step explanation:
what is the completely factored form of of this polynomial 81x^4 - 16y^4
Step-by-step explanation:
81x⁴ - 16y⁴
(9x²)² - (4y²)²
(9x² + 4y²)(9x² - 4y²)
(9x² + 4y²)(3x + 2y)(3x - 2y)
4 units to the left of -4 is
Answer:
-8
Step-by-step explanation:
If you were to do integer operations, then this question algebraically would mean -4-4=-8 because going to the left on a number line is meaning subtraction/negative and going to the right is addition/positve!
Therefore, the answer is -8 :)
please how do I find the answer
Answer:
7 of it is 12
Step-by-step explanation:
you have to plus the top ones
A water pipe has an outside diameter of 1 1/4 inches and a wall thickness of 5/16 inches. what is the inside diameter of the pipe?
Answer:
Step-by-step explanation:
There's a small trick here. You have to double the thickness. Why? Because the outside diameter goes through the thickness twice.
Inside diameter = outside diameter - 2 * thickness
outside diameter = 1 1/4 inches
thickness = 5/16
Inside diameter = 1 1/4 - 2 * 5/16
inside diameter = 5/4 - 10/16
Inside diameter = 5/4 - 5/8
Inside diameter = 10/8 - 5/8
Inside diameter = 5/8
-91.81 as a mixed number.
Answer: [tex]-91\frac{81}{100}[/tex]
Step-by-step explanation:
PLSSSS HELPPP ITS DUE TODAYYY!!!!!
A ball pit is filled with blue, red and yellow balls as shown in the photo. You reach in and randomly select one ball. Estimate the probability of this ball being yellow
Step-by-step explanation:
In my opinion I would say about 40% Because you can see 7 red balls on the top and 6 on the bottom. Hope This Helps.
please help timed this time i actually added picture
which exponential function is represented by the values in the table?
11x - 4 = 20 Solve for x
Answer:
24/11 approx 2.181818
Step-by-step explanation:
11x -4 = 20
11x= 20 +4
11x = 24
x = 24/11 approx 2.1818181818182
Answer:
x = [tex]\frac{24}{11}[/tex]
Step-by-step explanation:
Given
11x - 4 = 20 ( add 4 to both sides )
11x = 24 ( divide both sides by 11 )
x = [tex]\frac{24}{11}[/tex]
marking brainlist
please helpppp
Answer:
The answer is AB≠AC
SEMOGA MEMBANTU
r^2p÷5 ; p = -5, r = - 5
Answer:
=-5^2×(-5)÷5
=25×(-5)÷5
=-125÷5
=-25
I need 14 and 15 please give me the awnsers
Answer:
we know brainly.com/question/24497563?answering=true&answeringSource=feedPublic%2FhomePage%2F4
Step-by-step explanation:
Round the mixed number to the nearest whole or half.
8 4/27 this is a mixed number ok
PLEASE HELP
Answer:
8 jzhwwh8qoqqnsnwuwjwjqj
A. Graph A
B. Graph B
C. Graph
D. Graph D
Answer:
C
Step-by-step explanation:
y = (x-1) (x+4)
when y=0
x=1 and x= -4
so select C
Need help with all
Plzz
Answer:
i think and of a no is
a. √81/2.
on the left order the number from least to greatest.
on the right order the numbers from greatest to least.
PLEASE HELP
Answer:
square root of 4, 6.5, 6 and 2 thirds, 7, square root of 50, and 630%
(-3)^3, - square root if 65, -8.2, -8 and 2 fifths, - square root of 78, and -(3)^2
Nolan reads 14 pages per hour .After a total of 3 hours of reading this week,how many pages will Nolan have read in all
Relative to the cave opening, what integer represents the depth of the second
climber?
Answer:
what is the depth
Step-by-step explanation:
