The sum of the first (n) terms of the sequence is given by the formula (given below) . If this sequence is a geometric progression, find q. If this sequence is an Arithmetic progression, find d
Answers
Answer:Example 1:
Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.
S8=1(1−28)1−2=255
Example 2:
Find S10 of the geometric sequence 24,12,6,⋯.
First, find r.
r=r2r1=1224=12
Now, find the sum:
S10=24(1−(12)10)1−12=306964
Example 3:
Evaluate.
∑n=1103(−2)n−1
(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)
Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023
In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1. Then as n increases, rn gets closer and closer to 0. To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.
Example 4:
Find the sum of the infinite geometric sequence
27,18,12,8,⋯.
First find r:
r=a2a1=1827=23
Then find the sum:
S=a11−r
S=271−23=81
Example 5:
Find the sum of the infinite geometric sequence
8,12,18,27,⋯ if it exists.
First find r:
r=a2a1=128=32
Since r=32 is not less than one the series has no sum.
Step-by-step explanation:
Related Questions
Been stuck on this for hours, it's the Law of Sines. 25 POINTS!!
Answers
Answer:
Step-by-step explanation:
(Sin27) / 11 = (sin x) / 15
cross multiply
15 sin27 = 11 sin x
keep in calculator as you divide 15sin27 by 11.
sin x = .6190779542
do sin ^ -1 (.6190779542) (It’s a key on the calculator.)
x = 38.25*
9514 1404 393
Answer:
38.2°
Step-by-step explanation:
According to the equation you are give, ...
sin(x)/15 = sin(27°)/11
Multiplying by 15 gives you ...
sin(x) = 15·sin(27°)/11 ≈ 0.619078
The inverse sine function is used to find the angle x. It may show as sin⁻¹ on your calculator.
x = arcsin(0.619078)
x ≈ 38.2°
_____
Additional comment
x is shown in the figure as an acute angle, so that is the value we have chosen. The other angle that has sin(x) = 0.619078 is the supplement of this, or 141.8°. The two solutions are shown in the 2nd and 3rd attachments.
One week, Ethan earned $391.00 at his job when he worked for 23 hours. If he is paid the same hourly wage, how many hours would he have to work the next week to earn $102.00?
Answers
Answer:
6 hrs.
Step-by-step explanation:
So 391.00 can just be converted to 391 because they mean the same thing, so since we have $391 for 23 hrs, we can divde those, which gives us 17, this answer would show that Ethan earns $17 a hour, so if we divide how much he earns by the hour by how much money he could earn by next week ( 102/17), that would give us 6, Therefore, Ethan would need to work 6 hours for $102.00
Which of the following shows the correct solution steps and solution to
7x – 4 = –18?
A.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
2
2
7
x
7
=
−
2
2
7
x
=
−
2
2
7
7x−4
7x−4+4
7x
7
7x
x
=−18
=−18+4
=−22
=
7
−22
=
7
−22
B.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
1
4
7
x
−
7
=
−
1
4
−
7
x
=
2
7x−4
7x−4+4
7x
−7
7x
x
=−18
=−18+4
=−14
=
−7
−14
=2
C.
7
x
−
4
=
−
1
8
7
x
−
4
+
4
=
−
1
8
+
4
7
x
=
−
1
4
7
x
7
=
−
1
4
7
x
=
−
2
7x−4
7x−4+4
7x
7
7x
x
=−18
=−18+4
=−14
=
7
−14
=−2
D.
7
x
−
4
=
−
1
8
7
x
−
4
−
4
=
−
1
8
−
4
7
x
=
−
1
4
7
x
7
=
−
1
4
7
x
=
−
2
7x−4
7x−4−4
7x
7
7x
x
=−18
=−18−4
=−14
=
7
−14
=−2
Answers
Answer:
Simplify 7\times -47×−4 to -28−28.
-28=-18
−28=−18
2 Since -28=-18−28=−18 is false, there is no solution.
No Solution
So that it becomes 7x=-14
Divide both sides by 7
-14/7 is -2
So, x has a values of -2
Will give brainliest, Please explain how you got your answer!
Write an equivalent expression.
(x + 7) + 3y
Answers
What is the solution to the system of equations below?
y=-x+6 and y-x-6
O no solution
O infinitely many solutions
O (-18, 12)
O (18, 0)
Answers
Answer:
O (-18, 12)
Step-by-step explanation:
brainiest plz
Reduce to simplest form.
-5/8+(-8/5)=?
Answers
Answer:
[tex]-2\frac{9}{40}[/tex]
Step-by-step explanation:
[tex]-\frac{5}{8}+(-\frac{8}{5}) = -\frac{25}{40}-\frac{64}{40}[/tex] (find common denominator)
[tex]=-\frac{89}{40}[/tex]
[tex]=-2\frac{9}{40}[/tex] (reduce to simplest form)
Hope this helps :)
ARE THESE CORRECT YES OR NO TYPE ONLY IF YOU KNOW THANKS I REALLY NEED THIS!
Answers
Answer:
yes I think im not an expert but i think
Step-by-step explanation:
Answer:
Yes, all of them are correct.
what is the radius of x?
Answers
Answer:
To get the radius, divide the diameter by 2.
Answer:
to get the radius you have to divided the diameter by 2
Step-by-step explanation:
Help please please please
Answers
[tex]1/2=0.5\\5/0.5=10[/tex]
Which method could be used to estimate the growth rate of an exponential function from its graph?
-Divide the value of the function at x=3 by the value of the function at x=0, and then take the square root of the result.
-Divide the value of the function at x=2 by the value of the function at x=0, and then square the result.
-Divide the value of the function at x=2 by the value of the function at x=1, and then subtract the result from 1.
-Divide the value of the function at x=0 by the value of the function at x=1, and then subtract the result from 1.
Answers
Answer:
-Divide the value of the function at x=2 by the value of the function at x=1, and then subtract the result from 1.
Step-by-step explanation:
hope this help
pick me as the brainliest dont report me please
A watch decreased in price by
5/6. After the reduction it was priced at £11. What was the original price of the watch?
Answers
Answer:
66
Step-by-step explanation:
what is excess reagent
Answers
Answer:
We are commonly asked to find the extra reactants in a chemical equation. We can find it after balancing the equation and seeing the amount of moles that are present for each substance. Hence in chemistry and thermodynamic reactions it is the extra reactants that are not used up during the combustion process and therefore is excess of a said element.There are also limiting reagent which is the substance that limits the amount that can react and can be produced in a chemical reactionRate positively and give brainlist
The limiting reagent in a chemical reaction is a reactant that is totally consumed when the chemical reaction is completed. The amount of product formed is limited by this reagent, since the reaction cannot continue without it.
why is excess reagent used:
A good way to ensure that one reactant fully reacts is to use an excess of the other reactant. This is financially efficient when one of the reactants is very cheap. When one reactant is in excess, there will always be some left over.
how do you find the excess reagent:
The reactant that produces a lesser amount of product is the limiting reagent. The reactant that produces a larger amount of product is the excess reagent. To find the amount of remaining excess reactant, subtract the mass of excess reagent consumed from the total mass of excess reagent given
the temperature at noon at an Antarctic weather center was –15 °C. At midnight it had fallen by 12 °C. What was the temperature at midnight?
Answers
Answer:
-27 °C
Step-by-step explanation:
-15 -12 = -27
A System of Linear Equations consist of.....
O three or more lines.
O at least one line.
O at least two lines.
O more than two lines.
Answers
Answer:
B. At least one line
Step-by-step explanation:
Two lines can overlap on the coordinate plane, so it appears to be one line.
The total surface area of a cone whose radius is 2 r and slant height 2l is
(A) 2πr (l + r)
(B) πr (l + 4 r )
(C) πr (l + r)
(D) 2πrl
please answer urgent
Answers
Answer:
[tex]A=4\pi r(l+r)[/tex]
Step-by-step explanation:
The total surface area of a cone is given by :
[tex]A=\pi rl+\pi r^2\\\\=\pi r(l+r)[/tex]
Put r = 2r and l = 2l in the above formula
[tex]A=\pi \times 2r(2l+2r)\\\\A=2\pi r(2l+2r)\\\\=2\pi r \times 2(l+r)\\\\=4\pi r(l+r)[/tex]
Hence, the total surface area of the cone is [tex]4\pi r(l+r)[/tex].
What is the slope of AB?
Answers
Answer: -2/3
Step-by-step explanation:
If you want to find the slope of something, the quick way is to use [tex]\frac{rise}{run}[/tex].
In this situation, the “rise” (change in y axis) is -2 because it’s going down and the “run” (change in x axis) is 3. Therefore, it’s -2/3.
The formula to find slope is:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
(I think, if I memorized it correctly)
Which sample size would give the
best estimate of the population
mean?
Answer choices:
18
30
45
60
Answers
In an acute triangle, the measures of two angles are 50° and 60°. What is the measure of the third angle?
Answers
Answer:
70 degrees
Step-by-step explanation:
The measure of all angles in a triangle are 180 always
1. Add 50 + 60 = 110
2. 180 - 110 = 70
Hope that helps dude
A map of Utah has a scale of 1 cm: 30 mi. The border of Utah measures
about 3.7 cm. How long is the actual border of Utah and Wyoming? Show
your work to receive full credit
Answers
Answer:
The actual border of Utah and Wyoming is 111 miles long.
Step-by-step explanation:
We can use proportion to solve this!
[tex] \frac{1 \: cm}{30 \: mi} = \frac{3.7 \: cm}{x} \\ \\ \frac{111}{1} = \frac{1x}{1} \\ \\ 111 = x[/tex]
Please help me I’m so behind and I’m going to fail if I can’t get this answer. I need 15 but can someone also do 14.
Answers
Answer:
its d 100%
Step-by-step explanation:
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Get Ya free 25
Answers
Answer:
Ok
Step-by-step explanation:
Jack’s car used 18 gallons of gasoline to go 468 miles. At that rate, how many gallons would be used to go 754 miles? Explain how you know.
Answers
Answer:
29 gallons.
Step-by-step explanation:
For every gallon, a total number of 468/18 miles = 26 miles could be travelled.
And hence, to travel 754 miles, a total of 754/26 gallons = 29 gallons would be needed.
Hope this helped!
If a circle has a diameter of 30 meters, which expression gives its area in
square meters?
A. 30•n
B. 30^2•n
C. 15^2•n
D. 15•n
Answers
Answer:
C. 15²π
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Diameter: d = 2rArea of a Circle: A = πr²Step-by-step explanation:
Step 1: Define
d = 30 m
Step 2: Find Area
Substitute [D]: 30 m = 2rIsolate r: 15 m = rRewrite: r = 15 mSubstitute [AC]: A = π(15 m)²Rearrange: A = 15²πFor every | | followers Matthew has, Kevin has | |followers.
PLEASE HELP ILL MARK BRAINLEST
Answers
Answer:
For every 5 followers Mathew has, Kevin will have 10
Step-by-step explanation:
Answer:
For every 5 followers Matthew has, Kevin has 10 followers.
Step-by-step explanation:
A hybrid car can travel 40 miles per gallon. Approximately how many gallons of fuel will the car need to travel 20 km? (5 points) [1 mile = 1.6 km]
Answers
Answer:
To travel 20 Km, the hybrid car needs 0.3125 gallons of fuel.
Step-by-step explanation:
Proportions
The hybrid car can travel 40 miles per gallon.
Since one mile is equivalent to 1.6 Km, the distance traveled per gallon is 40*1.6 = 64 Km.
Now the distance is expressed in Km, we can find the gallons needed to travel 20 Km, by calculating 20/64 = 0.3125.
To travel 20 Km, the hybrid car needs 0.3125 gallons of fuel.
If x= −5, which equation is true?
a] 2x−4= −14
b] 3(4−x)=3
c] 2(x−4)= −14
d] 3(10−x)=21
Answers
2(-5) -4 = -14
-10 -4 = -14
-14 = -14
Shade row 3 and column C.
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Answer:
Shade in all of the boxes to the right of 3, and all of the boxes above the C.
What is the slope of the line? (Linear equations and slope quiz I-ready)
Answers
Answer: 2
Step-by-step explanation:
The slope of the linear graph in the question obtained using the ratio of the rise and run of the line is 2.
Recall :
Slope = Rise / Run
From the graph :
Rise = y2 - y1 = 5 - (-1) = 5 + 1 = 6
Run = x2 - x1 = 2 - (-1) = 2 + 1 = 3
The slope of the graph can be expressed thus :
Slope = Rise / Run = 6 /3 = 2Therefore, the slope of the line in the graph attached is 2
Learn more :https://brainly.com/question/18405415
50 points please help me with this. Dont spam random things. If your smart answer this please
Answers
Answer:
top one
Step-by-step explanation:
Answer: It's B.
Step-by-step explanation: this is 1st grade math. good luck!
If P=(-3,5) and Q=(1,9), find the midpoint of the segment PQ
Answers
Answer:
[tex](-1,7)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Step-by-step explanation:
Step 1: Define
Point P(-3, 5)
Point Q(1, 9)
Step 2: Find Midpoint
Simply plug in your coordinates into the midpoint formula to find midpoint
Substitute {MF]: [tex](\frac{-3+1}{2},\frac{5+9}{2})[/tex]Add: [tex](\frac{-2}{2},\frac{14}{2})[/tex]Divide: [tex](-1,7)[/tex]