There's a slight problem with your question, but we'll get to that...
Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by
• a (1) = 1
• a (n) = a (n - 1) + 21 … … … for n > 1
We can find the explicit rule for the sequence by iterative substitution:
a (2) = a (1) + 21
a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21
a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21
and so on, with the general pattern
a (n) = a (1) + 21 (n - 1) = 21n - 20
Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is
a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332
or more compactly,
[tex]\displaystyle\sum_{n=1}^N a(n) = 2332[/tex]
It's important to note that N must be some positive integer.
Replace a (n) by the explicit rule:
[tex]\displaystyle\sum_{n=1}^N (21n-20) = 2332[/tex]
Expand the sum on the left as
[tex]\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332[/tex]
and recall the formulas,
[tex]\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n[/tex]
[tex]\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2[/tex]
So the sum of the first N terms of a (n) is such that
21 × N (N + 1)/2 - 20N = 2332
Solve for N :
21 (N ² + N) - 40N = 4664
21 N ² - 19 N - 4664 = 0
Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead
N = (19 ± √392,137)/42 ≈ -14.45 or 15.36
so there is no positive integer N for which the first N terms of the sum add up to 2332.
The quadratic function f(x) has one zero at x=-5 and a turning point at (3,10). What is the value of its other zero?
The quadratic function [tex]f(x)[/tex] has one zero at [tex]x=-5[/tex] and a turning point at [tex](3,10)[/tex]. The value of other zero is [tex]11[/tex].
What is Quadratic function?The Quadratic function [tex]f(x)[/tex] is a polynomial function with one or more variables in which the highest power of the variable is two. i.e. [tex]f(x) = ax^{2} + bx + c[/tex]
What are zeros?The zeros of a polynomial [tex]f(x)[/tex] are all the [tex]x[/tex]-values that make the polynomial equals to zero. i.e. [tex]f(x)=0[/tex]
What is turning point?A turning point is a point at which the derivative changes sign.
We have,
One zero is [tex](-5)[/tex],
Let other Zero be [tex]"a"[/tex],
Turning point at [tex](3,10)[/tex].
i.e. [tex]x=3[/tex] and [tex]y=10[/tex]
Since the difference between [tex]3[/tex] and [tex](-5)[/tex] is [tex]8[/tex].
So,
The difference between the other zero from [tex]3[/tex] should be the same as the difference between [tex]3[/tex] and [tex](-5)[/tex].
i.e.
[tex]a-3=8[/tex]
[tex]a=11[/tex]
Hence the value of its other zero is [tex]11.[/tex]
To learn more about zeros click here
https://brainly.com/question/5975436
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Find the distance between the two points rounding to the nearest tenth (In decimal).
Answer:
approximately 8.9
Step-by-step explanation:
Regard (3, -2) and (7, 6) as the two acute angle vertices of a right triangle. The horizontal leg of this triangle has the length (7 - 3) = 4, and the vertical leg 6 - (-2) = 8.
Apply the Pythagorean Theorem to find the length of the diagonal connecting these two points. This length is the distance between the two points:
d = √(4² + 8²) = √(16 + 64) = √80 + √16√5 = 4√5, or approximately 8.9
A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (–4, 0) and (6, 0). The y-intercept of the first parabola is (0, –12). The y-intercept of the second parabola is (0, –24). What is the positive difference between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to the nearest tenth.
Answer:
.5
Step-by-step explanation:
Edge 2021
Answer:
It is indeed 0.5
Step-by-step explanation:
If you have this on edge, then it is correct.
Help plz!!
Ryan worked at a local ice cream shop during the summer. The money he earned for the first six weeks is given below.
$40, $80, $38, $40, $32, $65
Ryan then earned $24 in the seventh week. How were the mean and the median affected?
The mean decreased, and the median remained the same.
The median decreased, and the mean remained the same.
The median and the mean both remained the same.
The mean and the median both decreased.
Answer:
my answer isn't on the list, but doing the math the median increased from 39 to 40, but the mean decreased from 49.16 to 45.57
You deposit $100 in an
account that pays an
annual rate of 4%. How
much is in the account
after 12 years?
Answer:
5669.39
Step-by-step explanation:
Pls answer fast and no bs links or I’ll report
Answer:
Step-by-step explanation:
a c e
solve for x and y.
A x=6; y=10
B x=13.5; y=10
C x=6;y=5
D x=13.5; y=5
Answer:
B x=13.5; y=10
this is answer
Step-by-step explanation:
True or false 5(6 + 5) = (5 ×6) + (5 × 4)
Answer:
false
Step-by-step explanation
Find the value of sin^-1(4pi/5)
Answer:
No value because 4π/5 exceeds the domain
Step-by-step explanation:
The domain and range of sin^-1(x) is a domain of [-1,1] and a range of [-π/2,π/2]
Since 4π/5>1, this exceeds the domain and therefore has no value.
Okay can you guys help me find which one is the variable. And like what it means for like example x could equal to distance in km
Answer:
a) 1000+0.05x ≥2200
b) x=24000
Step-by-step explanation:
a) So we know that Nadia for certain gets paid $1000 each month. That is a concrete amount that doesn't change, so the variable (x) would be placed on the 5% she earns from sales. We don't know how much she sells each month because it varies, so that will be represented by the X. Her goal is to raise NO LESS than $2200, which means the amount she earns from sales has to be greater than or equal to $2200.
b) From here just solve the equation for X:
Can someone plz help me with the first one also it will be appreciated if u could show working out too!
Answer:
Angles in a quadrilateral add up to 360°.
[tex]90 + 3x + x + 20 + 2x + 10 = 360\\ 90 + 20 + 10 + 3x + x + 2x = 330\\ 120 + 6x = 360 \\ 6x = 360 - 120 \\ 6x = 240 \\ x = \frac{240}{6} \\ x = 40[/tex]
[tex]3x = 3 \times 40 = 120 \\ [/tex]
[tex]x + 20 = 40 + 20 = 60[/tex]
[tex]2x + 10 = 2 \times 40 + 10 = 80 + 10 = 90[/tex]
Difference between largest & smallest angles =
[tex]120 - 60 \\ = 60[/tex]
60 is the difference the largest & the smallest angle.
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is
1/8. There are 56 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answer:
There are 7 red marbles
Step-by-step explanation:
1/8=x/56
x= 56/8
x= 7
1. Alyssa is twice as old as Brittany, and Jazmin is 15 years older than Alyssa. If Jazmin is 45 years old, how old is Brittany?
Write two algebraic equations, let represent Alyssa’s age in years and represent Brittany’s age in years.
Tysm if u do this <3
Answer:
Brittany is 15 years old
Step-by-step explanation:
The way we get the answer is by getting the age of Alyssa 45-15=30 as, Jazmin is 15 years older than Alyssa and then we can see that Alyssa is twice as old as Brittany so we divide Alyssa's age by two. 30÷2=15 and we get Brittany's age which is 15 years old.
Leonard made the 3-d shape below for an art project. He wants to paint it blue.
How many square centimeters of paint does he need to paint the outside of every
side except for the bottom?
10 cm
6 cm
Answer:
90 [tex]cm^{2}[/tex] of blue paint
Step-by-step explanation:
From the given diagram, the sides have the same dimensions and the shape of a triangle.
Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height
Given that, the base of each side = 6 cm, and the height = 10 cm.
Then,
Area of each side of the shape = [tex]\frac{1}{2}[/tex] x 6 x 10
= 30 [tex]cm^{2}[/tex]
Since Leonard wish to paint only the 3 sides and not the bottom part of the shape, the amount of paint required can be determined as;
3 x area of each side = 3 x 30
= 90 [tex]cm^{2}[/tex]
Leonard would need 90 [tex]cm^{2}[/tex] of paint to paint the sides of the shape.
please help i don’t get it :(
If 9/10 is multiplied by 8/9 , will the product be greater than either of the two factors?
Answer:
No, both of the numbers are less than one whole and when you multiply them (I got 4/5) 4/5 is less than both of the factors.
Answer:
No
Step-by-step explanation:
It will not be because when a number is numtiplied by one, it stays the same. However, both of these are numbers less than 1, so the product will be smaller
our points are labeled on the number line.
Which point represents the value of ∣−12∣?
438467385378732452386236532168498329
Answer:
If the point is on positive 12 its that answer
Step-by-step explanation:
Carla and Marci are having a competition to see who can learn finish typing their research first. Carla already has 2 pages finished and can type 2 pages per hour. Marci has just started typing and can type 3 pages per hour. After how many hours will Carla and Marci have typed the same amount?
Answer:
The answer is 2 hours, if that i wrong then put in 3 hours.
Step-by-step explanation:
You could juat write out a chart for every number, so 2+0, 4+3, 6+6, so two hours.
Answer:
After 2 hoursStep-by-step explanation:
Let the time is x.
Carla will type:
2x + 2Marci will type:
3xSince they will have typed the same number:
3x = 2x + 23x - 2x = 2x = 2 hoursMr. Sweeney's car can travel 195 miles on 10 gallons of gas. How far
can Mr. Sweeney travel if he buys 18 gallons of gas?
I
Answer:
Miles in 10 gallons = 195
Miles in 1 gallon = 195/10 = 19.5
Miles in 18 gallons = 19.5 × 18 = 351 miles.
Answer:
Miles travelled by the car on 10 gallons of gas = 195 miles
Miles travelled by the car in 1 gallon of gas = 195 ÷ 10 = 19.5 miles
Miles travelled by the car in 18 gallons of gas = 19.5 × 18 = 351 miles.
Charlie has more than 50 game coins Charlie has 8 more than 3 times as game coins as Steven if x represents the number of game coins Steven has which inequality can be used to determine the possible number of game coins Steven has
Answer: [tex]x>14[/tex]
Step-by-step explanation:
Given
Charlie has more than 50 game coins
Steven has [tex]x[/tex] coins
So, according to the question, charlie has 8 more than 3 times the steven coins i.e.
[tex]\Rightarrow 3x+8[/tex]
Also, this must be greater than 50
[tex]\therefore 3x+8>50\\\Rightarrow 3x>42\\\Rightarrow x>14[/tex]
please find the sum of difference of (-12) + (-38)
will give brainliest
For the following right triangle, find the length x
Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
https://www.symbolab.com/solver/radical-equation-calculator/sin45%3D%5Cfrac%7B5%7D%7Bx%7D
Please help and please dont send a link of the answer to a website :)
Answer:
well we know that top and botton are 12 and the sides are 5. there are 4 sides soo thats 4 times 5. so basically its 12x12x5x5x5x5 whick is 90000.
Step-by-step explanation:
sorry for the wait!
hope this helps!
please mark brainliest!
have a good day!
:) ;)
(if this is wrong im so sorry, i tried .;(
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answer:
12:32
Step-by-step explanation:
there are twelve triangles n-32 total shapes
Is -2.2, -1.1, 0.1, 1.3,... an arthmetic sequence
Answer:
answer is no
Step-by-step explanation:
People r so annoying. Delete my answer bc no step by step¿
Fine. In order o make this an arithmetic sequence, the difference between each number should be the same. It’s not same in this sequence
Mr. Gurney purchased 3 dozen
eggs for $5.73. How much would it
cost to buy 5 dozen eggs?
Please tell me how to solve this and the answer :)
Which question is a statistical question because it has more than one answer?
1 : “ where does the current u.s president live?”
2: “ what size coat am i wearing now ?”
3: “did jack wear sneakers or boots to school today?”
4: “ What size shirt the kids in the school wear?”
What is the GCF of 12,18, 24
Answer:
6
Step-by-step explanation:
12/2=6
18/3=6
24/4=6
1) Alicia's gross monthly pay is $1,700.
Alicia pays 5.7% of her monthly salary for
Social Security. How much does Alicia
pay?
A $0.96
C $96.90
B $9.69
D $969.90
Answer:
96.90
Step-by-step explanation:
1700x.0570=96.90
1a. what is the slope. 1b. what is the y- intercept 1c. write the equation. PLEASE HELP IM DOING HOMEWORK AND ITS 1:00am
the slope is 1 cos its goin ovr one, up one
y-int is (0,3) or jus strait up 3 cos thts where it crosses the y
iiiif you write it using y=mx+b,, m is the slope n b is the y int so itd jus be: y=x+3