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
svlad2 [7]
2 years ago
9

Determine if the sequence 4, 10, 19, 31,... is arithmetic. If it is, determine the first term a and the common difference d

Mathematics
2 answers:
dmitriy555 [2]2 years ago
8 0

Answer:

  not an arithmetic sequence

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers that have a common difference. That is, the difference between any term and the previous term is constant for the sequence. Other kinds of sequences have other relationships between the differences.

<h3>Differences</h3>

The "first" differences of this sequence are ...

  • 10-4 = 6
  • 19-10 = 9
  • 31 -19 = 12

The first differences are not constant. However, we notice the "second" differences are constant. These are the differences of successive first differences.

  • 9 -6 = 3
  • 12 -9 = 3 . . . . . . constant 2nd differences

<h3>Sequence type</h3>

The first differences are not constant, so this sequence is not an arithmetic sequence.

For polynomial sequences, the level of constant difference tell you the degree of the polynomial describing the sequence. This sequence has constant 2nd-level differences, so can be described by a 2nd degree (quadratic) polynomial:

  f(n) = 1.5n² +1.5n +1 . . . . . a quadratic sequence

__

<em>Additional comment</em>

Sequences that are <em>exponential</em> have differences that have a common <em>ratio</em>. That ratio is the same at every level. It is the base of the exponential function.

max2010maxim [7]2 years ago
7 0

Answer:

It is not arithmetic, so therefore there is no common difference

Step-by-step explanation:

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. There is no constant term in the above pattern.

You might be interested in
Refer to the figure to complete the proportion A/C = Y/?
salantis [7]
Hello,
Please, see the attached file.
Thanks.

3 0
3 years ago
Two supplementary angles are in a ratio of 1:2, What is the measure of the large
ElenaW [278]
The large angle = 120 degrees
Supplementary angles are two angles whose measures add up to 180°
Since we know from the ratio that one angle is twice the size of the other, the angles have to be 60 and 120.
4 0
3 years ago
X^2-8x+16=5 what are the solutions?
svp [43]
Hey!


The first step to solving this equation would be to subtract 5 from both sides of the equation.

<em>Original Equation :</em>
x^{2} - 8x + 16 = 5

<em>New Equation {Added Subtract 5 to Both Sides} :</em>
x^{2} - 8x + 16 - 5 = 5 - 5

Now we solve our new equation.

<em>Old Equation :</em>
x^{2} - 8x + 16 - 5 = 5 - 5

<em>Solution {Old Equation Solved} :</em>
x^{2} - 8x + 11 = 0

The next step would be to solve with the quadratic formula.

<em>Quadratic Equation ( 1 ) :</em>
x =  \frac{-(-8) +  \sqrt{(-8)^{2} -4 * 1 * 11 } }{2*1}

<em>Quadratic Equation ( 1 ) {Solved} :</em>
4 + \sqrt{5}

<em>Quadratic Equation ( 2 ) :</em>
x =  \frac{-(-8) -  \sqrt{(-8)^{2}-4 *1*11 } }{2*1}

<em>Quadratic Equation ( 2 ) {Solved} :</em>
4 - \sqrt{5}

<em>So, our final solutions for the equation x^{2} - 8x + 16 = 5 are...</em>

x = 4 + \sqrt{5}

<em>and </em>

x = 4 - \sqrt{5}

Hope this helps!


- Lindsey Frazier ♥
5 0
4 years ago
What are the next three terms -14,-9,-4
Serggg [28]
-28, -18, -8 ehhheheheeheh
5 0
3 years ago
Give an MN find the value of X and Y
Sever21 [200]

9514 1404 393

Answer:

  • x = 21
  • y = 114

Step-by-step explanation:

Consecutive interior angles are supplementary:

  (6x +6)° +(3x -15)° = 180°

  9x -9 = 180 . . . . . . . . . . . . . . simplify, divide by °

  x -1 = 20 . . . . . . . . . . . . divide by 9

  x = 21

__

Angles of a linear pair are supplementary:

  (3x -15)° +(y +18)° = 180°

  3(21) -15 + y + 18 = 180 . . . . substitute for x, divide by °

  y = 114 . . . . . . . . . . . . . . . . . . subtract 66

7 0
3 years ago
Other questions:
  • Solve x^2+x-6=0 (will mark brainliest)
    8·2 answers
  • I would like to know what 1.34 as a fraction in simplest form would be
    12·1 answer
  • Need Help!!!!!!!! If x = 2.5, 5x = ____. (Only input decimals such as 12.7 as the answer.)
    6·2 answers
  • triangle BCD is a right triangle the length of the hypotenuse is 20 cm the length of one of the legs is 15 cm what is the length
    5·1 answer
  • Write the equation of a like that is parallel to y=6x+1 and that passes through the point -7,1
    5·1 answer
  • Which of the symbols correctly relates the two numbers below? check all that apply 13?13
    9·1 answer
  • Sorry but need help there is 3 more questions
    10·2 answers
  • You have $50. You have some $5 bills and some $10
    11·1 answer
  • Please help me answer this question thank you :)
    7·1 answer
  • What if the bag did not tell us how many total servings and only told us how many total cups?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!