1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
skelet666 [1.2K]
3 years ago
15

A playground is being designed where children can interact with their friends in certain combinations. . If there is 1 child, th

ere can be 0 interactions. . If there are 2 children, there can be 3 interactions. . If there are 3 children, there can be 9 interactions. . If there are 4 children, there can be 18 interactions. . Which recursive equation represents the pattern? (2 points)
Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
7 0

The <em>correct answer</em> is:

The general term would be given by: T_n=\frac{3}{2}(n-2)(n-1)

Explanation:

We first find the first differences between the terms of this sequence:

3-0 = 3; 9-3 = 6; 18-9 = 9

Since these are not the same, we must find the second differences (differences between the first diferences):

6-3 = 3; 9-6 = 3

these are the same, so this will be a quadratic sequence. This will be of the form T_n=an^2+bn+c. The value of <em>a</em> will be half of the second difference, which is 3; this means <em>a </em>will be 3/2.

Using the term numbers as n, for the first term, we have:

T_1=\frac{3}{2}(1^2)+b(1)+c=0 \\ \\=\frac{3}{2}+b+c=0

For term 2,

T_2=\frac{3}{2}(2^2)+b(2)+c=0 \\ \\=\frac{3}{2}(4)+2b+c=0 \\ \\=\frac{12}{2}+2b+c=0 \\ \\=6+2b+c=0

Taking these as a system of equations gives us:

\left \{ {{\frac{3}{2}+b+c=0} \atop {6+2b+c=0}} \right.  \\ \\\text{Subtracting the second equation from the first gives us:} \\ \\ \left \{ {{\frac{3}{2}+b+c=0} \atop {-(6+2b+c=0)}} \right. \\ \\ \text{This gives us:} \\ \\-4.5-b=0 \\ \\\text{Solving this for b, we add 4.5 to each side:} \\ \\-4.5-b+4.5=0+4.5 \\-b=4.5 \\ \\\text{Divide-b both sides by -1:} \\\frac{-b}{-1}=\frac{4.5}{-1} \\b=-4.5

This gives us:

T_n=\frac{3}{2}n^2-\frac{9}{2}n+c=0 \\ \\\text{For term #1, we have} \\ \\T_1=\frac{3}{2}(1^2)-\frac{9}{2}(1)+c=0 \\T_1=\frac{3}{2}-\frac{9}{2}+c=0 \\\frac{-6}{2}+c=0 \\-3+c=0 \\-3+c+3=0+3 \\c=3

This gives us:

T_n=\frac{3}{2}n^2-\frac{9}{2}n+3

This factors to:

T_n=\frac{3}{2}(n-2)(n-1)

polet [3.4K]3 years ago
3 0
<span>We are given with:when n=1, a(1) = 0 n=2, a(2) =3 n=3, a(2) =9 n=4, a(2) =18The equation that suits the conditions is a(n) = a(n-1) + (n-1)*3</span>
You might be interested in
A principal amount of $4,700 is deposited into an account paying interest at a rate of 3%, continuously compounded. What will be
Ronch [10]

The account balance after 3 years if the interest is compounded continuously is $5,142.62

<h3>How to find compound interest?</h3>

  • Principal, P = $4,700
  • Time,t = 3 years
  • Interest rate, r = 3%

r = 3/100

r = 0.03 rate per year,

A = Pe^rt

A = 4,700.00(2.71828)^(0.03)(3)

= 12,775.916^0.09

A = $5,142.62

Therefore, the account balance after 3 years if the interest is compounded continuously is $5,142.62

Learn more about compound interest:

brainly.com/question/24924853

#SPJ1

8 0
2 years ago
Find the value of z please help
Elza [17]

z + 93 = 180

z = 87

Answer z = 87

Here are the answer for x and y, in case you need them.

x = 2* 93 - 112

x = 186 - 112

x = 74

y = 2 * 80 - x

y = 160 - 74

y = 86

6 0
3 years ago
Read 2 more answers
PZ PLZ PLZ HELP I DO NOT UNDERSTAND THIS KINDA OF STUFF IF U DONT KNOW DO NOT ANSWER IT I ACTUALLY NEED HELP NO LINKS PLZ PLZ
ivanzaharov [21]

Answer:

176

Step-by-step explanation:

11x11=121

12x11=132

9=20-11

16-9=7

11x16=176

Hope this helped you :D

And pls give me brainlist if you can

7 0
3 years ago
Read 2 more answers
Which is the only strategy down below that does NOT work when figuring out what 30% of 2,000 is?
ozzi

Answer:

C. 0.03 x 2000

6 0
3 years ago
Read 2 more answers
Suppose you went to a carnival. the price in was $6, and you paid $0.50 to get on each ride. if you went to the carnival and rod
Maksim231197 [3]
You'd do $0.50 × 11 = $5.50 which is the total cost for the rides, and then you'd add $6 to make $11.50 which is the total amount you spent.
7 0
3 years ago
Read 2 more answers
Other questions:
  • 2 centimeters on the map represents 100 kilometers
    10·1 answer
  • To place and as in a newspaper, it cost $8 plus $0.75 for each line. Write and evaluate an expression to find the total cost for
    5·1 answer
  • Nathaniel mowed 18 lawns in 3 hours. What was his rate of mowing in hours per lawn?
    7·1 answer
  • To celebrate ratios, Mrs. Johnson’s class will make pizzas. Julio is in charge of bringing in the sauce. There are 30 students i
    12·2 answers
  • Factor : 2b^2 + 13b - 7<br><br>Please help !!! :)
    12·1 answer
  • A total of 432 tickets were sold for the school play. They were either adult tickets or student tickets. There were 68 fewer stu
    8·1 answer
  • Kerry and her brother and noticed there is 3/4 of a pint of ice cream in the freezer. After they eat some ice cream there is 1/3
    13·1 answer
  • HELP HELP HELP HELP HELP<br> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    12·2 answers
  • Do research to find a species that used to be endangered but no longer is considered endangered
    12·1 answer
  • 1.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!