Answers
Part A
A geometric sequence is where the terms increase by the same ratio.
Example:
7, 14, 28, 56, ...
We start at 7 and double each term to get the next term. The common ratio is 2.
============================================================
Part B
The next step is to subtract the two equations straight down. This will cancel the vast majority of the terms, and allow to solve for [tex]S_n[/tex] to get a fairly tidy formula. Refer to part C for more info.
============================================================
Part C
[tex]S_n = a_1 + a_1r + a_1r^2 + \ldots + a_1r^{n-1}\\\\rS_n = a_1r + a_1r^2 + \ldots + a_1r^{n-1} + a_1r^n\\\\rS_n - S_n = \left(a_1r + a_1r^2 + \ldots + a_1r^{n-1}+a_1r^n\right)-\left(a_1 + a_1r + a_1r^2 + \ldots + a_1r^{n-1}\right)\\\\S_n(r - 1) = a_1r^n - a_1\\\\S_n = \frac{a_1r^n - a_1}{r-1}\\\\S_n = \frac{-a_1(r^n - 1)}{-(-r+1)}\\\\S_n = \frac{a_1(1-r^n)}{1-r}\\\\[/tex]
For more information about the canceling going on from step 3 to step 4, see the attachment below.
Related Questions
Researchers capture and mark 43 squirrels in a park. The next week, researchers capture 50 squirrels and 38 of them are marked from the previous month. Estimate the squirrel population in the park.
Answers
The question is an illustration of sample and population, and the estimate of the population of squirrel in the park is 55
How to determine the population of squirrel?The given parameters are:
Marked squirrels = 43
Captured squirrels = 50
Of the 50 captured squirrels, 38 are from the marked squirrels.
This means that the number of unmarked squirrels is:
Unmarked = 50 - 38
Evaluate
Unmarked = 12
The population of the squirrel is then calculated using:
Population = Marked + Unmarked
So, we have:
Population = 43 + 12
Evaluate the sum
Population = 55
Hence, the estimate of the population of squirrel in the park is 55
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Quadrilateral ABCD has vertices at A(-4,5) B(-1,9) C(7,3) and D(4,-1). What is the most precise name for a quadrilateral ABCD?
Answers
Answer:
Rectangle
Step-by-step explanation:
The answer you put was a rhombus , which is wrong . if you put the coordinates in you would see that its a rectangle slightly tilted instead of rhombus , a rectangle has more of a wider side than a rhombus does . please change your answer!
Find the area of the figure. Use 3.14 for 77.
in
7 in
A. 56.13 in2
B. 35.13 in2
C. 70.26 in2
D. 49,26 in2
Answers
Answer:
C 70.26 in2
Step-by-step explanation:
6 = D
R = D/2
R = 3
A = 3.14 x 3 x 3
A = 3.14 x 9
A = 28.26
The area of the triangle is
A = 6 x 7
A = 42
So
42 + 28.26
70.26 in2
help math highschool
Answers
Answer:
Your answer is d) 3, 7, 8.
Step-by-step explanation:
s and t are parallel and r is transversal.
4 and 3 are congruent as the vertical angle.
4 is 7 is alternative exterior angles.
4 and 8 are corresponding angles.
Jalen bought 4 pizzas. He also spent $8 on wings. He paid a total of $60. He can use the equation 4p + 8 = 56 to determine the price of each pizza. How much was each pizza?
Answers
Answer:
13 dollars a pizza because if you put 4x13 that is 52 then add the wings 8$ that is your answer 60....
Step-by-step explanation:
Hopefully It helped ya... (:
Answer:
p = 12
Step-by-step explanation:
Given:
Jalen bought 4 pizzas. He also spent $8 on wings. He paid a total of $60. He can use the equation 4p + 8 = 56 to determine the price of each pizza.
To Find:
How much was each pizza?
Solution:
Since it already given a equation thus we can just solve using the equation given:
4p + 8 = 56
Subtract 8 from both sides
4p + 8 = 56
- 8 -8
-----------------------
4p = 48
Divide both sides by 4
4p/4 = 48/4
p = 12
Hence, each pizza cost $12.
Kavinsky
which expressions are equivalent to 4^-2*7^-2
Answers
Answer:
[tex]\textsf{B)}\quad \dfrac{1}{28^2}[/tex]
[tex]\textsf{C)} \quad \dfrac{7^{-2}}{4^2}[/tex]
Step-by-step explanation:
[tex]4^{-2} \cdot 7^{-2}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b \cdot c^b)=(ac)^b:[/tex]
[tex]\implies (4 \cdot 7)^{-2}[/tex]
[tex]\implies (28)^{-2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{28^2}[/tex]
-------------------------------------------------------------------------------------------
Also,
[tex]4^{-2} \cdot 7^{-2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{7^{-2}}{4^2}[/tex]
[tex]\\ \rm\Rrightarrow 4^{-2}7^{-2}[/tex]
a^{-n}=1/a^n[tex]\\ \rm\Rrightarrow \dfrac{1}{4^2.7^2}[/tex]
a^n×b^n=(ab)^n[tex]\\ \rm\Rrightarrow \dfrac{1}{(4.7)^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{28^2}[/tex]
If we break only 4
[tex]\\ \rm\Rrightarrow \dfrac{7^{-2}}{4^2}[/tex]
Option B and C
Look at
Which of the following is the best description for this type pair of angles?
Answers
Answer:
Complementary angles
Step-by-step explanation:
Complementary angles because the two angles is shared on a same line as each others.
Michael's total sales last month
was $12,000. If he earned $480 in
commission, what was his
commission rate?
Answers
480/12000=.04
Draw the circle with equation x² + y² = 16
Answers
Answer:
Below.
Step-by-step explanation:
The center of the circle is at the origin and its radius is √16 = 4.
So set a compass to 4 and draw a circle with the compass point at the origin.
I think it’s
True
False
True
False
True
Answers
Answer:
False
False
True
True
True
Step-by-step explanation:
Answer:
False
False
True
True
True
Step-by-step explanation:
up ;)
Please help!! Will mark brainlyest.
Answers
Answer:
1 and 2
Step-by-step explanation:
Find the midpoint of CD.
C = (-3,4) and D = (5,-8)
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 -3}{2}~~~ ,~~~ \cfrac{ -8 + 4}{2} \right)\implies \left(\cfrac{2}{2}~~,~~\cfrac{-4}{2} \right)\implies (1~~,~~-2)[/tex]
1
1. The measure of 2G is 82º. What is the
measure of its supplement?
Answers
So the supplement is 98°
Answer:
98º
Step-by-step explanation:
Since a supplementary angle is 2 angles which equal 180 degrees we would have this angle and 1 more angle that add up to 180:
[tex]82+x=180[/tex]
subtract 82 from both sides
[tex]x=98[/tex]
TIME SENSITIVE I REALLY NEED HELP
Which function is continuous at x = 18?
Answers
Answer:
The answer is D.
Step-by-step explanation:
a) Plugging x = 18 gets numerator 0^2/18 = 0 that not continuous.
b) Plugging x = 18 the denomiator becomes a value/0 making it undefined.
c) Plugging x = 18 gets tan(2pi) = 0/1 which is 0
d) f(x) = 36 is should be a straight lines at y =36. I think. Best option is D.
500ml of milk for 60p
4 litres for £3.20
Which bottle is better value for money?
Answers
Answer:
4 liters for £3.20
Step-by-step explanation:
we want to maximize quantity for each unit of money spent. if we use mL and p, we want to maximize mL/p
500 mL = 60 p
divide both sides by 60p to get a mL/p value
500 mL/60 p = 50/6 p ≈ 8.3 mL per pence
4 L = £3.20
note:
1000 mL = 1L
divide both sides by 1 L/ 1000 mL
1000 mL / 1 L = 1
1 L / 1000 mL = 1
100 p = £1
divide both sides by 100p / £1
100p / £1 = 1 = £1 / 100p
convert everything to the same units (mL and p) to accurately compare
4 L = £3.20
4L = 4L * 1 = 4L * 1000 mL / 1 L = 4000 mL. Note that we have two options to choose from -- 1000 mL / 1 L and 1 L / 1000 mL. We choose the first one here because we want the 4L to cancel out with the 1 L
£3.20 = £3.20 * 1 = £3.20 * 100p / £1 = 320 p. note we put the £1 on the bottom so the euros cancel out.
thus,
4 L = £3.20
= 4000 mL = 320p
divide both sides by 320p to get a mL / p value
4000 mL / 320 p = 12.5 mL/p
8.3 mL per pence in the first one
12.5 mL per pence in the second one
the second one has a higher mL per pence, so that is a better value
Each day, a salesperson earns $25 plus 5% of their total sales for the day. The salesperson's goal is to earn more than $50 on Thursday. Which statements are true? Select all that apply.
Answers
The true statement about the inequality is that Total sales per day is greater than $250
How to write and solve inequality equation?Total sales per day = xAmount earned per day = 25 + 5% of x= 25 + 0.05x
Thursday = 4th day of the weekThe inequality:
4(25 + 0.05x) > 50
100 + 0.2x > 50
100 - 50 > 0.2x
50 > 0.2x
x > 50/0.2
x > $250
Learn more about inequality:
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Miss David's birthday is in April, and she is going to have a party. She is
looking to buy a bag of decorations. Each bag has two different types of
decorations: balloons and streamers. The first bag has 10 balloons and 4
streamers. The second bag has 12 balloons and 5 streamers. The last bag
has 8 balloons and 10 streamers. Bag 1 costs $82, bag 2 costs $100, and
bag 3 costs $120.
How much does each type of decoration cost?
How did you get your answer?
what equation did you use?
Answers
Answer:
120
Step-by-step explanation:u need to add it all and divide 4
which of the following is an example of the atmosphere inracting with the biosphere
Answers
Answer:
rain (hydrosphere) falls from clouds in the atmosphere to the lithosphere and forms streams and rivers that provide drinking water for wildlife and humans as well as water for plant growth (biosphere)
Step-by-step explanation:
Jacob is twice as heavy as Ken Linda is half as heavy as Ken Giver 3 children is at least 35 kg. a By letting Linda's mass be x, write an inequality for the total mass of the 3 children b. Hence, find the minimum mass of Ken Monica wanted to buy x notebooks at $3.50 each and 15 rulers at $(x+0.20) each She had a budget of $105 only c. Write an inequality for Monica's total expenditure . Hence, how many notebooks can she buy at most?
Answers
==> she can buy 45 notebooks at most.
[tex] \: \: \: \: [/tex]
What is the percent of change 30in to 24in
Answers
Answer:
1/5
Step-by-step explanation:
30 - 24 = 6
6 = 6/30
6/30 = 1/5
Answer: 20%
Step-by-step explanation: 30- 24 = 6
6/30 × 100/ 1 = 20%
PLEASE help me
this is a 45°-45°-90° triangle.
solve for a.
Answers
Answer:
a = 8
Step-by-step explanation:
45° - 45° - 90° triangle
1 - 1 - √2
8 - 8 - √8
50 POINTS
What is the value represented by the letter E on the box plot of the data?
45, 45, 50, 55, 60, 65, 72, 75, 80, 80, 90
Answers
Answer:
90
Step-by-step explanation:
In a box plot, the point farthest to the line is the greatest or maximum number of the problem(in this case E). You look for the greatest number out of them all and that would be your answer(90).
Can i pretty please with a cherry on top get brainliest??
:>
Emma has 23 teddy bears. Noah has 17 teddy bears. How many teddy bears do they have in all?.
Answers
Answer:
40
Step-by-step explanation:
23 + 17
= 40
can someone pls help me !!
Answers
Answer:
I am not sure
Step-by-step explanation:
I believe if you take and break down what you paid and then it will be easier to figure out the interest
Allen is showing his work in simplifying –8.3 + 9.2 – 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning. Write feedback to Allen explaining the mistake he made and how to correct his work.
Step Work Reasoning
−8.3 + 9.2 − 4.4 + 3.7 Original problem
1 −8.3 + 9.2 + 4.4 + 3.7 Additive inverse
2 −8.3 + 4.4 + 9.2 + 3.7 Commutative property
3 −8.3 + (4.4 + 9.2 + 3.7) Associative property
4 −8.3 + 17.3 Simplify
5 9 Simplify
Answers
Answer:
0.2
Step-by-step explanation:
A 15kg bag of strawberry for $8
Answers
Answer:
see below
Step-by-step explanation:
Not sure what you are looking for :
15 kg / $8 = 1.875 kg per dollar
$8 / 15 kg = .533 dollars per kilogram
Answer number 11 please thank you
Answers
Answer:
A. No
B. No
C. Yes
D. No
jfzisossyokszkvgtis
Identify the area of the polygon with vertices & C(3,3) A(8,-2). S(3,-4), and H(0, -2)
A = 31.5 units^2
A = 28 units^2
A = 25 units^2
A = 35.5 units^2
help me solve this w/work!! tyyyy
Answers
The vertices of the polygon form a trapezoid, and the area of the polygon is 28 unit squares
How to determine the area of the polygon?The vertices are given as:
C = (3,3)
A = (8,-2)
S = (3,-4)
H = (0, -2)
The area of the polygon is calculated using:
[tex]A = \frac 12 \sum\limits^{n-1}_{k = 0}(x_ky_{k+1} - y_kx_{k+1})[/tex]
So, we have:
A = 1/2 * |(3 * -2 - 8 * 3 + 8 * -4 - 3 * -2 + 3 * -2 - 0 * -4 + 0 * 3 -3 * -2)|
Evaluate
A = 1/2 * |-56|
Remove the absolute bracket
A = 1/2 * 56
Evaluate the product
A= 28
Hence, the area of the polygon is 28 unit square
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Joe, a plumber, charges $45 per hour plus
$100 for making an in-home visit. Write
and solve an equation to find out how
many hours of plumbing work are needed
Answers
Answer: The answer is five
Step-by-step explanation:
Set y = z
50x + 75 = 65x
Subtract 50x from both sides
50x (-50x) + 75 = 65x (-50x)
75 = 15x
Divide both sides by 15
75 (/15) = 15x (/15)
5 = x
And there we have it, x = 5! So it takes 5 hours of work for each to cost the same.
Answer: (Y - 100)/ 45 =No of hours
where y is the full payment
Step-by-step explanation:
Charges per hour plus visit is 45+100 where 100 Is fixed
2hr is (45 × 2) +100
Payment y for Xhrs= 45X + 100
Y =45X + 100
Y -100 =45X
Y -100/45 = X
Please help :( Algebra 2 Question
A child arranges toy action figures into rows. The first row has three action figures and each row after the first has six more figures than the row before it. Write a rule for the number of action figures in the nth row. If there are nine , how many action figures are there?
Answers
Answer:
number of action figures = 3 + 6(n-1)
at n = 9: number of action figures = 51
Step-by-step explanation:
first row: 3
second row: 6 more than the row before it (3) = 6 + 3 = 9
third row: 6 + 9 = 15
arithmetic series: [tex]a_n = a_1 + (n-1)d[/tex], where
[tex]a_n[/tex] is the nth term in the output
[tex]a_1[/tex] is the first output
n is the input
d is the difference between terms
here, we are given the row, and we want to figure out the number of action figures. thus, row = input and number of action figures = output.
the first output, in the first row, is 3
the difference between the number of action figures in each row is 6
thus, our formula is
[tex]a_n = 3 + (n-1)6 = 3 + 6(n-1)[/tex]
when the row is 9, the number of action figures is equal to
3 + 6(9-1) = 3 + 6 * 8 = 51