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
Gwar [14]
2 years ago
5

Determine the formula for the nth term of the sequence:-2,1,7,25,79,...​

Mathematics
1 answer:
rodikova [14]2 years ago
5 0

A plausible guess might be that the sequence is formed by a degree-4* polynomial,

x_n = a n^4 + b n^3 + c n^2 + d n + e

From the given known values of the sequence, we have

\begin{cases}a+b+c+d+e = -2 \\ 16 a + 8 b + 4 c + 2 d + e = 1 \\ 81 a + 27 b + 9 c + 3 d + e = 7 \\ 256 a + 64 b + 16 c + 4 d + e = 25 \\ 625 a + 125 b + 25 c + 5 d + e = 79\end{cases}

Solving the system yields coefficients

a=\dfrac58, b=-\dfrac{19}4, c=\dfrac{115}8, d = -\dfrac{65}4, e=4

so that the n-th term in the sequence might be

\displaystyle x_n = \boxed{\frac{5 n^4}{8}-\frac{19 n^3}{4}+\frac{115 n^2}{8}-\frac{65 n}{4}+4}

Then the next few terms in the sequence could very well be

\{-2, 1, 7, 25, 79, 208, 466, 922, 1660, 2779, \ldots\}

It would be much easier to confirm this had the given sequence provided just one more term...

* Why degree-4? This rests on the assumption that the higher-order forward differences of \{x_n\} eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of \{x_n\} by \Delta^{k}\{x_n\}. Then

• 1st-order differences:

\Delta\{x_n\} = \{1-(-2), 7-1, 25-7, 79-25,\ldots\} = \{3,6,18,54,\ldots\}

• 2nd-order differences:

\Delta^2\{x_n\} = \{6-3,18-6,54-18,\ldots\} = \{3,12,36,\ldots\}

• 3rd-order differences:

\Delta^3\{x_n\} = \{12-3, 36-12,\ldots\} = \{9,24,\ldots\}

• 4th-order differences:

\Delta^4\{x_n\} = \{24-9,\ldots\} = \{15,\ldots\}

From here I made the assumption that \Delta^4\{x_n\} is the constant sequence {15, 15, 15, …}. This implies \Delta^3\{x_n\} forms an arithmetic/linear sequence, which implies \Delta^2\{x_n\} forms a quadratic sequence, and so on up \{x_n\} forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.

You might be interested in
Find the product<br> 876 greater or equal to 65 =
Salsk061 [2.6K]
Greater ..............
8 0
3 years ago
Read 2 more answers
A solution of salt and water is 20% salt. If 25% of the water is removed, what is the percentage of salt in the new solution?
Ratling [72]
So lets say that this salt and water solution consists of 100 liters.

Then that means 20 liters is salt, and 80 liters out of the 100 is water.



Now, we remove 25% of the water. 25% of 80 liters is 20 liters. So, we are left with 80-20, or 60 liters.



Now in all we have 20 liters of salt, and 60 liters of water.

The percentage of salt in the new mixture will be 20/(20+60) = 20/80 = 25%.



Your answer is 25%
4 0
3 years ago
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will sea
spin [16.1K]

Answer:

83 adult tickets and 217 student tickets.

Step-by-step explanation:

Let number of adult tickets sold = x

Given that total number of tickets = 300

So, number of student tickets = 300 - x

Cost of adult ticket = $15

Cost of student ticket = $11

Total collection from adult tickets = $15x

Total collection from student tickets =  (300-x)\times 11 = 3300-11x

Given that overall collection = $3630

15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow   x = 82.5

So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.

Now , collection = $3632

4 0
3 years ago
Find the Distance between points A and B: A (8, 12) B: (2, 4)
mote1985 [20]
ANSWER-the distance is (6,8)
if you set the equation up from 2-8=6 which is your x value and 4-12=8 is your y value it should also give you your Distance between the two points
4 0
2 years ago
Is it possible to make a triangle with measure of 3mm 9mm and 5mm​
tatyana61 [14]

Answer: No

Step-by-step explanation: if you mean the measure of a is 3, the measure of b is 9 and the measure of c is 5, c being the hypotenuse then the answer is no because the the sides of a and b must be less than the measure of c. If 5 wasn’t the hypotenuse then the answer would be different.

(KEEP IN MIND THAT IF 9 IS THE HYPOTENUSE THEN THE ANSWER IS YES)

Hope this helps! :)

4 0
3 years ago
Other questions:
  • Help quick please!! Thanks
    12·2 answers
  • How much extra money did a typical person earning $50,000 receive due to the tax cuts?
    5·1 answer
  • What is the value of x?
    6·1 answer
  • A cone has a slant height of 10 centimeters and a lateral area of 60π square centimeters. what is the volume of a sphere with a
    5·1 answer
  • A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school coll
    8·1 answer
  • Jeremy has 3 yards of ribbon to use for wrapping gifts he cuts the ribbon into pieces that are one fourth yard long how many pie
    12·2 answers
  • 1. If x is the supplementary angle of 155°,
    7·1 answer
  • Identify each line or segment that intersects ⊙ T. HELP PLEASE!!!
    15·1 answer
  • POOOOOOOOOG PLZZZZ!!!! DUE IN TEN MINUTES!!!!! HELP WILL DO BRAINLIEST!!! IMPORTANT!!!
    14·1 answer
  • If the diameter of a circle is 80 ft., find the area A 5,024 ft2 B 20,096 ft2 C 251.2 ft2 D 125.6 ft2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!