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
Shkiper50 [21]
2 years ago
7

Use differences to find a pattern in the sequence.

Mathematics
1 answer:
frez [133]2 years ago
8 0

Answer:

  220

Step-by-step explanation:

You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.

<h3>First differences</h3>

Subtracting each term from the next, we find the sequence of first differences to be ...

  5, 7, 13, 23, 37, 55

<h3>Second differences</h3>

The first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.

The second differences are the differences of the sequence of first differences. They are ...

  2, 6, 10, 14, 18

<h3>Third differences</h3>

The differences of the terms of the 2nd-difference sequence are constant: 4.

  4, 4, 4, 4, 4

Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.

<h3>Next term</h3>

Since we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.

  next 2nd difference = 18 +4 = 22

  next 1st difference = 55 +22 = 77

  next sequence term = 143 +77 = 220

The eighth term should be 220.

__

<em>Additional comment</em>

The n-th term is ...

  f(n) = 2/3n^3 -3n^2 +28/3n -4

You might be interested in
Chips suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing.
Artyom0805 [142]
(a) P( fifth one is bad)  = P( first 4 are OK) * P(5th is bad)

= (0.98)^4 * 0.02 =  0.0184   or 1.84%

(b)  this will be (0.98)^10 =  81.70%



4 0
3 years ago
Which function has a range of {yly &lt; 5}?
Alexeev081 [22]

Answer:

f(x) = -(x-4)^2 + 5

Step-by-step explanation:

The function f(x) = -(x-4)^2 + 5 is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.

Proving that f(x) = -(x-4)^2 + 5 \le 5 for all x:

x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.

8 0
3 years ago
An interior angle of a regular polygon is eleven times its exterior
Rainbow [258]

I think they answer might be ....... /7

5 0
3 years ago
Help need this answered.
SashulF [63]

Answer:

C

Step-by-step explanation:

C

6 0
2 years ago
HELP PLEASEEEE!!!!! [Easy]
sertanlavr [38]

Answer:

180

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • The area of a closet floor measures 3 yards by 3 yards and each custom tile that makes up the flooring is 1 1/2 square feet. How
    6·2 answers
  • What is 1 and 3/4 divided by 4/5​
    5·1 answer
  • What is the volume of the pyramid in the diagram?
    5·1 answer
  • a bag contains blue, green, yellow, and red marbles. The probability of drawing a yellow marble is 3/20. What is the probability
    13·1 answer
  • The area of a square can be found using the equation A = s², where A is the area and s is the measure of one side of the square.
    11·2 answers
  • (THIS IS A TEST I NEED HELP)
    13·2 answers
  • Solve for x. Round to the nearest tenth, if necessary. 5.5 D 61° х F<br><br>Please help​
    8·1 answer
  • 6x-2y=-2
    14·2 answers
  • What is lemma?<br> ________________<br> Thx!
    14·2 answers
  • Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume define
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!