The nth terms of sequence 1 ; 5 ; 11 ; 19 is n² + n + -1 and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3 .
What is quadratic sequence?The differences (referred to as first differences) between every two successive terms are the same, then it is called an arithmetic sequence (which is also known as a linear sequence). But if the first differences are NOT same, and instead, the second differences are the same, then the sequence is known as a quadratic sequence.
According to the question
The sequence 1 , 5 , 11 , 19
First difference : 4 6 8
Second difference: 2 2
1.1.1>
Now, expression for the nth term of the sequence.
Quadratic equation
ax² + bx + c
at n= 1
a + b + c = 1 -----------------(1)
At n = 2
4a + 2b + c = 5 ------------------(2)
At n = 3
9a + 3b + c = 11 -------------------(3)
solving equation
Subtracting equation (3) from (2)
9a + 3b + c = 11
-4a - 2b - c = -5
5a + b = 6 ----------------------(4)
Subtracting equation (2) from (1)
4a + 2b + c = 5
-a - b - c = -1
3a + b = 4 ---------------------------- (5)
Subtracting equation (5) from (4)
5a + b = 6
-3a - b = -4
2a = 2
a = 1
Putting value in equation (5)
3a + b = 4
3*1 + b = 4
b = 1
Substituting the value in equation (1)
a + b + c = 1
1 + 1 + c = 1
c = -1
Substituting the value in the quadratic equation
x² + x + -1
For nth term
n² + n + -1
1.1.2>
Term of the sequence is 2549
Now,
using the nth term
n² + n + -1 = 2549
n (n+1) = 2550
n (n+1) = 50 * 51
n = 50
1.2> sequence of numbers is given: -2 ,-3 ,-6 ,-11
First difference = -1 -3 -5
Second difference = -2 -2
1.2.1 >
Now , expression for the nth term of the sequence.
Quadratic equation
ax² + bx + c
at n= 1
a + b + c = -2 -----------------(1)
At n = 2
4a + 2b + c = -3 ------------------(2)
At n = 3
9a + 3b + c = -6 -------------------(3)
solving equations
Subtracting equation (3) and (2)
9a + 3b + c = -6
-4a - 2b - c = 3
5a +b = -3 ----------------(4)
Subtracting equation (2) and (1)
4a + 2b + c = -3
-a - b - c = 2
3a + b = -1 -------------------(5)
Now,
Subtracting equation (5) and (4)
5a +b = -3
-3a - b = 1
2a = -2
a = -1
Putting value of a in equation (5)
3*-1 + b = -1
b = 2
Substituting values in equation (1)
-1 + 2 + c = -2
c = -3
nth term
-n² + 2n -3
1.2.2>the sequence of numbers will never contain a positive term.
because its first term is -ve and difference between consecutive term is always -ve. or as per nth term n² is a -ve term .
Hence, the nth terms of sequence 1 ; 5 ; 11 ; 19 is n² + n + -1 and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3 .
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write an equation for the nth term of the arithmetic sequence. Then find a40.
1/4,1/2,3/4,1,...
Answer:
The nth term is: [tex]a_n = \frac{1}{4} + \frac{1}{4}(n-1)[/tex]
a40 = 10
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.
The nth term of a sequence is given by:
[tex]a_n = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
1/4,1/2
This means that:
[tex]d = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}[/tex]
1/4
This means that [tex]a_1 = \frac{1}{4}[/tex]
The nth term is:
[tex]a_n = a_1 + (n-1)d[/tex]
[tex]a_n = \frac{1}{4} + \frac{1}{4}(n-1)[/tex]
Then find a40.
[tex]a_{40} = \frac{1}{4} + \frac{1}{4}(40-1) = \frac{1}{4} + \frac{39}{4} = \frac{40}{4} = 10[/tex]
So
a40 = 10
X+2y=7 x+5=3y what is resulting equation
Find an equation of the circle having the given center and radius.
Center (-7, 6), radius 6
Answer:
36 = (x+7)^2 + (y-6)^2
Step-by-step explanation:
6^2=(x-(-7))^2 + (y-6)^2
At the beginning of the year, Evelyn had $30 in savings and saved an additional $12 each week thereafter. Cooper started the year with $75 and saved $7 every week. Let E E represent the amount of money Evelyn has saved t t weeks after the beginning of the year and let C C represent the amount of money Cooper has saved t t weeks after the beginning of the year. Write an equation for each situation, in terms of t , t, and determine the interval of time when Evelyn has more in savings than Cooper.
Answer:
E=12t+30 C=7t+75
Evelyn has more in savings than Cooper when t > 9 weeks.Step-by-step explanation:
Please, my whole grade depends on this question!!!
Answer:
y = 14.4x - 18.4
Step-by-step explanation:
This is the equation for the regression line, I hope this helps!
Pls awnser i will give brailiest
Answer:
A. 124
Step-by-step explanation:
first i found the area of the circle which is 113
then i multiplied that which gave me 452
then i used what's given "6" for a half circle and multiplied it by 4 and that gave me the size of one side of the square 24
then i multiplied 24 x 24 which is 576 the area of the square
lastly i subtracted 576-452
Brainliest pls
Hey, can someone please help me? I’m pretty sure the answers are B and D but I just wanna make sure.
Answer:
yes b and d
Step-by-step explanation:
3. An artist is creating a sculpture from clay. He starts with clay in the shape of a sphere with a radius of 3 inches.
What is the approximate volume of the clay sphere the artist started with?
Answer:
Step-by-step explanation:
The volume of the clay sphere the artist started with is 113.04 in^3
What is the volume of the clay sphere?We know that the artist starts with a sphere of clay with a radius of 3 inches, and we want to find the volume of clay that he has.
Then we just need to find the volume of the sphere.
Remember that for a sphere of radius R, the volume is:
[tex]V = (4/3)*3.14*R^3[/tex]
In this case, R = 3 in, replacing that we get.
[tex]V = (4/3)*3.14*(3 in)^3 = 113.04 in^3[/tex]
The volume of the clay sphere the artist started with is 113.04 in^3
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find the erea of the trapezoid.
Answer:
36
Step-by-step explanation:
A (base) 6
B (Base) 12
H (height) 4
Allison flipped a coin twenty times. She flipped heads 4 times and tails 16 times. What is the experimental probability that Allison will flip heads on her next flip?
The answer choices are:
80%
25%
20%
Please help!!
Answer:
C. 20%
Step-by-step explanation:
4 times out of 20 is 20%
Acone has a volume of 967 cubic feet. If the radius is 6
feet, what is the height of the cone?
Answer:
25.65
Step-by-step explanation:
9. Waldo and Freddy caught fish one weekend. The dot plots show the lengths of the fish they caught. Length of Waldo's Fish + 16 15 17 18 19 20 21 22 Inches Length of Freddy's Fish
The Range of the length of the fish caught by Freddy is Greater than the range of the length of the fish caught by Waldo.
Step-by-step explanation:
Please help anybody due in LESS THAN 1 MIN!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
distance was 35 units and the average speed was 5 units per minute
Step-by-step explanation:
-47--12=-35
the absolute value of -35 is 35
35 units took 7 minutes
so 1 unit takes 35/7 minutes= 5 minutes
Please Help me i'm not good with math
Good drivers have a quiet level of efficiency in their actions; this derives from a) a good level of attention Ob) accurate observation Oc) both Od) nelther
Answer:
d. all of the above
Step-by-step explanation:
just took driving course test
Good drivers exhibit a quiet level of efficiency in their actions, which stems from a combination of a good level of attention and accurate observation (option c).
Firstly, a good level of attention means being fully focused and attentive while driving, avoiding distractions, and being aware of the surroundings. This allows drivers to anticipate potential hazards, respond quickly to changing situations, and make informed decisions. Secondly, accurate observation involves keenly observing the road, traffic, and other relevant factors, such as signs, signals, and pedestrians.
By accurately observing their surroundings, good drivers can assess risks, maintain proper positioning, and execute maneuvers with precision. The combination of attention and observation enables drivers to anticipate and respond effectively, promoting safety, efficiency, and smooth execution of actions on the road. The correct option is c.
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Don’t waste an answer if you ain’t gonna help :)
423 inches = _________ feet, _________ inches
Answer:
432 inches = 35 feet and 3 inches
solve for x in kite
Answer:
x = 38
Step-by-step explanation:
since angle AED is a right angle 2x + 14 = 90
subtract 14 from 90 you get 76, divide that by 2 you get 38
Use the geometric series 5^Ž (8)*-* to answer each question.
n=1
What are the terms in the series?
1 + 8 + ___+ ____+ ____
Answer:
First one is:
1 + 8 + 64 + 512 + 4096
Second one is:
73
Answer:
First one is:
1 + 8 + 64 + 512 + 4096
Second one is:
73
Step-by-step explanation:
The scale on a map states that 1 centimeter corresponds to 20 kilometers. On the map, two cities are 0.3 cm apart. Find the actual distance.
Answer: The actual distance is 6 km
Step-by-step explanation: If you do a conversion from 1 cm to 20 km in fraction form, you will have
[tex]\frac{1cm}{20km} = \frac{0.1cm}{km ?}[/tex]
So, if you solve for km, you will get 6 using cross multipulcation
Which graph is defined by the function given below?
y = (x + 2)(x + 7)
118
10
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answer:
Graph A
Step-by-step explanation:
the zeros of the function are
0=x+2 x=-2
and
0=x+7 x=-7
so the graph where the function crosses those two points at y=0
Evaluate the expression: -4a2 + 3ab - (2a + 3b) if a = 1/4 and b = -12
Enter answer as a decimal.
Answer:
Value of equation = 26.25
Step-by-step explanation:
Given:
Equation given
-4a² + 3ab - (2a + 3b)
Given value of a = 1/4
Given value of b = -12
Find:
Value of equation
Computation:
-4a² + 3ab - (2a + 3b)
By putting value of a and b
-4(1/4)² + 3(1/4)(-12) - [2(1/4) + 3(-12)]
-4(1/16) - (36/4) - [2/4 - 36]
-4/16 - 36/4 - [-142/4]
- 0.25 - 9 + 142/4
-0.25 - 9 + 35.5
Value of equation = 26.25
Find the circumference and the area of a circle
with the dimensions listed. Use the value 3.14 for π
,and do not round your answers. Be sure to
include the correct units in your answers.
a) diameter of 3 cm
b) radius of 5 ft
In response to the question, we may say that As a result, the radius of the circle is 9.42 cm and its area is 7.065 cm sq
What is circle?A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.
a) 3 cm diameter: The radius (r) of a circle is half its diameter, hence r = 3 cm/2 = 1.5 cm
The formula C = 2r gives the circumference of a circle, where is approximately equivalent to 3.14.
As a result, C = 2 3.14 1.5 cm = 9.42 cm.
The formula A = r2 calculates the area of a circle.
As a result, A = 3.14 (1.5 cm)2 = 7.065 cm sq.
As a result, the radius of the circle is 9.42 cm and its area is 7.065 cm sq
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WILL MARK BRAINLIEST PLEASE HELP!!!
A right circular cone is intersected by a plane that passes through the cone's vertex and is parallel to its base, as in the picture below. What is produced from this intersection?
A. A Pair of intersecting lines
B. A Parabola
C. A Point
D. A Pair of parallel lines
Answer:its D. A pair of parallel lines
Step-by-step explanation:
Answer: parallel lines
Step-by-step explanation:
Alguien que hable español??
Six friends went apple picking.
They picked a total of 49 pounds
of apples that they shared equally.
How many pounds of apples did
each one take home?
find the area of a circle whose diameter is 7cm
Answer:
3.5pi
Step-by-step explanation:
just multiply together and you'll get your answer
Answer:
38.5 cm^2
Step-by-step explanation:
Diameter ( d ) = 7 cm
Radius ( r ) = 7 / 2 cm
Formula : -
Ar ( circle ) = π r^2
π r^2
= ( 22 / 7 ) x ( 7 / 2 )^2
= ( 22 / 7 ) x ( 49 / 4 )
= 38.5 cm^2
Complete the equation of the line through (4,-8) and (8,5)
Use exact numbers.
Y=?
The Answer:
y=3.25x+ (-21)
Answer:
y-intercept = (0, -21)
Step-by-step explanation:
Find the value of the slope.
[tex]m = \frac{13}{4} [/tex]
Find the value of the y-intercept.
[tex]b = - 21[/tex]
List the slope and y-intercept.
Slope: 13/4
y-intercept: (0, -21)
Answer choices
40%
50%
What is the answer please help if you put a link I will report you I’m being dead freaking serious
Answer:
50%
Step-by-step explanation
add the total and divide 35 (flowers sold by 5th graders) over 70 (total number of flowers sold by all 3 grades)
GUYS HELP PLEASE ASAP You are deciding between two jobs. Offer 1 is $40,000 and a raise of
$4,000 per year. Offer 2 is $52,000 and a raise of $2,000 per year. In how
many years will both jobs pay you the same salary? What would the salary
be? Which offer should you choose if you plan on working for 10 years?
Answer:
offer 1= you get 80k for the first offer for 10 years.
offer 2= you get 72k for the second offer for 10 years.
Result:
offer one would be better as you would get more money.