Answers
The explicit formula for calculating the sum is
[tex]S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}[/tex]
The sum of the nth term of a sequence is expressed as;
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
a is the first term
d is the common difference
n is the number of terms
For the sequence 0 + 1 + 2 + 3 +...
[tex]S_n=\frac{n}{2}(2(0)+(n-1)1)\\S_n= \frac{n}{2}(n-1)\\S_n= \frac{n(n-1)}{2}[/tex]
Similarly for the sequence:
1 + 2+ 3 + 4+...
[tex]S_n=\frac{n}{2}(2(1)+(n-1)1)\\S_n= \frac{n}{2}(2+n-1)\\S_n= \frac{n(n+1)}{2}[/tex]
Taking the product of the sum to get the explicit formula for calculating the sum
[tex]S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}[/tex]
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Related Questions
Abcd is a parallelogram determine the length of BE
A)51 units
B)102 units
C)96 units
D) -11 units
Answers
Answer:
B) 102 units
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. This means ...
BE = ED
3 -9x = -8x +14
-11 = x . . . . . . . . . . . . add 9x -14
BE = 3 -9x = 3 -9(-11) = 3 +99
BE = 102 units
Is 5.12 times 10n =512
Answers
Answer:
it is D
Step-by-step explanation:
I have to show you, but if I do it don't on the paper
I will give Brainliesttttt :D!
A car's gas mileage is the distance it can go using 1 gallon of gas (measured in miles per gallon).
Based on the graph, what is this car's gas mileage? Explain.
Answers
Answer:
20 mpg
Step-by-step explanation:
Answer:
The car is traveling 20 miles per gallon.
Step-by-step explanation:
There are two ways you can solve this.
1) Since this is a graph of the car's gas mileage, all you have to do is look to find the miles for one gallon, which is plotted in this case. As you can see, for one, it is plotted halfway between 0 and 40, so that means the mile number would be 20. Looking at this, the car travels 20 miles per gallon.
2) You can also look at the point at the top that is clearly defined, and the point is (12, 240), 12 gallons used for 240 miles. To get the exact number of miles for one mile, you would divide 12 and 240 both by 12, which results in (1, 20). Since it is miles per gallon, the car gas mileage is 20 miles per gallon.
Hope this helped and have a great day!
Dan received 64 dollars for his birthday. He went to a sporting goods store
and bought a baseball glove, baseball, and bat. He had 31 dollars left over,
how much did he spent on the baseball gear?
Answers
Answer:
the answer is 33 bucks because you have subtract the 64 -31 =33
We can create an Algebraic equation to represent the scenario. The variable “x” is equal to how much of his birthday money he spent.
64-x=31 [Equation]
64-64-x=31-64 [Subtract 64 from both sides to cancel it out and isolate x]
-x=-33 [Simplification after subtraction]
-x/-1=-33/-1 [Divide by -1 on both sides to cancel it out and solve for x]
x=33 [Defined Variable]
*Recall that “x” is equal to his expenses.
Therefore, Dan spent $33 of his $64.
We can check this because 64-33=31.
Please give Brainliest
tammy has soccer practice every 12 days, basketball 18 days, band practice 20 days, and music class every 24 days. If she has all these practices on the same day today, then how many days will it be until she has all four practices.
Answers
Answer:
360 days
Step-by-step explanation:
It would be a whole year until the classes line up on the same day again, because it would only be the exact same date of the next year that they line up.
Hope this helps!
The owner of a bookstore buys used books from customers for one dollar and 50 Cent each owner then resells the used books for 400% of the amount he paid for them what is the price of a used book in the bookstore?
Answers
1.50 x 4 = 6
It takes 6 fruit pickers 18 hours to pick a field of fruit. How long would it take 8 fruit pickers to pick the same field.
Answers
Time taken by [tex]8[/tex] fruit pickers to pick the fruits of the same field is equals to [tex]13.5[/tex]hours.
What is time?" Time is defined as the continues process which help us to measure the period/ length of occurring of event. It does not have any dimensions."
According to the question,
Time take by [tex]6[/tex] fruit pickers to pick the fruit from the field [tex]= 18[/tex]hours
As per the given situation we have,
Time taken by[tex]8[/tex] fruit pickers to pick the fruits of the same field
[tex]=\frac{(6)(18)}{8}[/tex]
[tex]=13.5[/tex]hours
Hence, time taken by [tex]8[/tex] fruit pickers to pick the fruits of the same field is equals to [tex]13.5[/tex]hours.
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Review
Directions: What does each of the following mean? Write out in words and phrases.
Example: 7 - 12 means: seven minus twelve
1. 11 + t
2. 7rst
3. t - 17
4. (10)(n)
5. 15 * y
6. 4x
7. a + b
8. 14x + 3y
Answers
Answer:
1. Eleven plus t
2. 7 times r times s time t
3. t minus seven
4. ten times n
5. fifteen times y
6. four times x
7. a plus b
8. fourteen times x plus 3 times y
Step-by-step explanation:
Hope this helps!
Answer:
1, eleven plus t
2, seven rst
3,t-17
........................
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y=−2x−5
y=2x−2
Answers
Answer:
This doesn't make since.
Step-by-step explanation:
One card is selected at random from a deck of card. Determine the probability that card selected is not a 7( simplify your answer)
Answers
Answer:
P(~7) = 12/13
Step-by-step explanation:
There are 4 sevens in a normal deck of cards.
Therefore there are 48 cards out of 52 that are not 7.
P(~7) = 48/52 simplified, it is 12/13
I need help on this
Here it is
Answers
2. Barlow School: (4 / 9) * 873 = 388 of the students are boys.
873-388 = 485 of the students are girls.
The b(boy) to g(girl) ratio at Barlow School is 388b:485g
1. Willow School: (2 / 3) * 630 = 420 of the students are girls.
630-420 = 210 of the students are boys.
The b(boy) to g(girl) ratio at Willow School is 420g:210b
3. 388 - 210 = 178
Answer: Barlow School has the greater number of boys by 178 students.
Solve the equation: q –10 = -10
Answers
Answer:
No solution
Step-by-step explanation:
The co-efficient, in this case the - 10s, cancel each other out, leaving just q
Write the equation (y=mx+b) that represents the relationship show on the graph.
Answers
Answer:
y= 3x + 4
Step-by-step explanation:
yeah-ya....... right?
Alyssa is baking a cake the recipe calls for 8 cups of flour she already put in 2 cups how many more cups does she need to add
Answers
Students are running in a relay race. Each team will run a total of 3 miles. Each member of a team will run 1/3 mile
How many students will a team need to complete the race? Circle the correct number below
Answers
Answer:
9 students
Step-by-step explanation:
If 1 student runs a 3rd we need 3 students to run 1 mile.
Since we need 3 times that amount of miles we multiply the amount of students it takes to run 1 mile so that we find out how many we need to run 3 miles.
3 x 3 = 9
They will need 9 students I hope this helps have a great day :)
Please lots of points I wasn’t at school when this was taught
Answers
Answer:
4x+2=4x+4, no solution
Step-by-step explanation:
first, i'm assuming the flower bed is a square so that all 4 sides are x+1. next, to find the perimeter you have to add up the side lengths of each shape.
vegetables: x + x+1 + x + x+1 = 4x+2 so the perimeter of the vegetables must be 4x+2
flowers: x+1 + x+1 + x+1 + x+1 = 4x+4
since the two must be equal, we have 4x+2=4x+4, this is the equation Trent can use
next, to solve the equation, subtract 4x from both sides to get 2=4. this obviously isn't true so there is no solution
NEED ASAP
in a company, 65% of workers are men. if 1,995 people work for the company who aren’t men, how many worker are their in all.
Answers
Answer:
5700
Step-by-step explanation:
Assume that the total number of people working for the company is x. Since 65% of workers are men and 1,995 people working for the working are not men, then that means that 35% of the total number of people working for the company is equal 1,995.
Set up an equation: 0.35x = 1,995 and find x.
x = 5700
Robert earns $498.00 for 40 hours of work. How much does he earn if works 30 hours at the same pay rate? Do not round your answer.
Answers
Answer:$373.50
Step-by-step explanation:
$498.00 divided by 40 is 12.45
12.45 times 30 is $373.50
see image above ^^^^
Answers
Triangle ABC was rotated 90 degrees counter clockwise to become triangle STU
Can you help me solve this please.
Answers
Answer:
23
Step-by-step explanation:
First, divide the figure into a large rectangle (2 * 5), a small rectangle (3 * 2), and a quarter circle with a radius of 3. Adding the areas of the 3 shapes together we get 10 + 6 + 7 = 23.
[LARGE RECTANGLE]
A = w * l = 2 * 5 = 10 ([tex]units^{2}[/tex])
[SMALLER TRIANGLE]
A = w * l = 3 * 2 = 6 ([tex]units^{2}[/tex])
[QUARTER CIRCLE]
A * [tex]\frac{1}{4}[/tex] = πr² * [tex]\frac{1}{4}[/tex] = 3 * 3 * π * [tex]\frac{1}{4}[/tex] = 7 ([tex]units^{2}[/tex])
6=4x^3-10x^2 please hurry it's a test
Answers
Answer:
x = about 2.705
Step-by-step explanation:
Does this help? Are you supposed to find x? That's what I did but you don't state what exactly you need.... So.....?
What is 34÷18? Explain or show your reasoning.
Answers
Answer:
1.8889
Step-by-step explanation:
HELP ME PLEASE ASAP ASAP
Answers
Ln(x)+ln(x+7)=1
solve this log equation
Answers
Is 0.225 a rational number?
Answers
Answer:
Maybe
Step-by-step explanation:
maybe
Answer:
yes because it can be written as a fraction 225/1000
How much is f(x) = 3(4)x
Answers
Answer:
f ( x ) = 12 x
Step-by-step explanation: 3x4=12 so that makes it f(x)=12x
2(x + 1) - 3x
howwwwwww
Answers
Answer:
a = -x + 2
Step-by-step explanation:
First, you must distribute to get 2x + 2 and adding in the -3x it equals 2x + 2 - 3x = a
Combine the like terms to get -x + 2 = a
Since there is 2 variables then the answer will stay a = -x + 2 because x or a must be substituted in order to find the other variable
Can someone put an answer for each box plzzzz.
Answers
what has a fraction in numerator, denominator or both???
Answers
is this linear or not and why
Answers
Answer:
YesStep-by-step explanation:
Both equations of this system are of degree one.
They are both linear as the graph of both is a line.
Answer:
yes
Step-by-step explanation:
The highest power of variable is 1 . So it is a linear equation of two variables .