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What are the first three terms of a sequence of the fourth and fifth terms are 27 and 39 and the second differences are a constant 2?
Given that the second differences of the sequence are a constant 2, the sequence can be modeled as a quadratic function. The general form of a quadratic sequence is ( an^2 + bn + c ). With the fourth term being 27 and the fifth term being 39, we can set up equations to find the coefficients. Solving these, we find that the first three terms of the sequence are 15, 21, and 27.
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Which finite differences are constant for a quartic function?
For a quartic function, the second and fourth finite differences are constant. The first finite differences will vary, while the second differences, representing the change in the first differences, will become constant. The fourth differences will also be constant because the quartic function is a polynomial of degree four.
What is the rule for quadratic sequences?
A quadratic sequence is a sequence of numbers in which the difference between consecutive terms changes at a constant rate. To identify the rule, first calculate the first differences (the differences between consecutive terms) and then the second differences (the differences of the first differences). If the second differences are constant, the sequence is quadratic. The general form of a quadratic sequence can be expressed as ( an^2 + bn + c ), where ( n ) is the term number, and ( a ), ( b ), and ( c ) are constants.
What sequence is formed from difference of differences between terms of a sequence?
These are called the second differences. If they are all the same (non-zero) then the original sequence is a quadratic.
How do I find the nth term in a quadratic sequence?
To find the nth term in a quadratic sequence, first identify the first and second differences of the sequence. The second difference should be constant for a quadratic sequence. Use this constant to determine the leading coefficient of the quadratic equation, which is half of the second difference. Next, use the first term and the first difference to derive the complete quadratic formula in the form ( an^2 + bn + c ) by solving for coefficients ( a ), ( b ), and ( c ) using known terms of the sequence.
How is a arithmetic sequence found?
You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.
Which finite differences are constant for a quartic function?
For a quartic function, the second and fourth finite differences are constant. The first finite differences will vary, while the second differences, representing the change in the first differences, will become constant. The fourth differences will also be constant because the quartic function is a polynomial of degree four.
If the first differences of a sequence are a constant 4 and the second term is 8 what are the first 5 terms of the sequence?
4,8,12,16,20
What sequence is formed from difference of differences between terms of a sequence?
These are called the second differences. If they are all the same (non-zero) then the original sequence is a quadratic.
How do I find the nth term in a quadratic sequence?
To find the nth term in a quadratic sequence, first identify the first and second differences of the sequence. The second difference should be constant for a quadratic sequence. Use this constant to determine the leading coefficient of the quadratic equation, which is half of the second difference. Next, use the first term and the first difference to derive the complete quadratic formula in the form ( an^2 + bn + c ) by solving for coefficients ( a ), ( b ), and ( c ) using known terms of the sequence.
How is a arithmetic sequence found?
You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.
What are a geometric sequence?
A geometric sequence is an ordered set of numbers such that (after the first number) the ratio between any number and its predecessor is a constant.
What are first differences?
The first differences for a sequence Un is the set of numbers Dn = Un+1 - Un They are the set of numbers obtained by subtracting the first number from the second, the second from the third, and so on.
What is the nth term for the sequence 5 15 29 47 69?
To find the nth term of the sequence 5, 15, 29, 47, 69, we first determine the differences between consecutive terms: 10, 14, 18, and 22. The second differences are constant at 4, indicating that the nth term is a quadratic function. By fitting the quadratic formula ( an^2 + bn + c ) to the sequence, we find that the nth term is ( 2n^2 + 3n ). Thus, the nth term of the sequence is ( 2n^2 + 3n ).
What actors and actresses appeared in Blade af Satans bog - 1920?
The cast of Blade af Satans bog - 1920 includes: Karina Bell as Naimi (fourth sequence) Hugo Bruun as Count Manuel (third sequence) Nalle Halden as The Majordomo (second sequence) Erling Hanson as John (first sequence) Hallander Helleman as Don Gomez de Castro (second sequence) Carl Hillebrandt as Rautamiemi (fourth sequence) Halvard Hoff as Jesus (first sequence) Wilhelm Jensen as Carpenter Tenna Kraft as Marie Antoinette (third sequence) Vilhelm Petersen as Fouquier-Tinville (third sequence) Elith Pio as Joseph (third sequence) Clara Pontoppidan as Siri (fourth sequence) Sven Scholander as Michonnet (third sequence) Jacob Texiere as Judas (first sequence) Jeanne Tramcourt as Lady Genevive de Chambord (third sequence) Viggo Wiehe as Count de Chambord (third sequence) Emma Wiehe as The Countess of Chambord (third sequence) Carlo Wieth as Paavo (fourth sequence)
What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54 respectively?
It could be -3 or +3.
What is a recursive sequence and its relationship to a Fibonacci sequence.?
A recursive sequence uses previous numbers to find the next number in a sequence after the base case. The Fibonacci sequence is an example of such a sequence. The base numbers of the Fibonacci sequence are 0 and 1. After that base, you find the next number in the sequence by adding the two previous numbers. So, the Fibonacci sequence looks like so: 0, 1, 1, 2, 3, 5, 8.... So, the third number is found by adding the first and second numbers, 0 and 1. So the third number is 1. The fourth number is found by adding the second and third numbers, 1 and 1. So, the fourth number is 2. You can continue on this way forever.
What is the nth term for -9 -6 -1 6 15?
The given sequence is -9, -6, -1, 6, 15. To find the nth term, we can observe that the differences between consecutive terms are increasing by 3: (-6 - (-9) = 3), (-1 - (-6) = 5), (6 - (-1) = 7), (15 - 6 = 9). The second differences are constant at 2, indicating a quadratic relationship. The nth term of this sequence can be expressed as ( a_n = n^2 + 2n - 10 ).
