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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?
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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 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 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.
How do you solve the formula of a sequence of numbers.?
It is impossible to "solve" the formula since you will be given only a finite number of values. If you are given k values then there is a polynomial of order (k-1) that will generate those values, and infinitely more polynomials of higher order which will do so. Furthermore, there are non-polynomial functions that will do the trick as well.Having said that, there are some things you can do towards solving the formula. The question is usually answered using Occam's razor: if there are two or more possible solutions, use the simpler one.If the question mentions arithmetic sequence, then you know that each term in the sequence is equal to the preceding term plus some constant (which may be negative). This is known as the "common difference".The position to term formula for an arithmetic sequence is:U(n) = a + d*n for the nth term,where n is a counter that locates the term in the sequence (n = 1, 2, 3, ...)d is the common difference anda is the 0th term. That is, the term that would have come before the first term if you continued the sequence for one step in the reverse direction.There are polynomial sequences, where the first round of calculating differences between successive terms does not yield a constant but differencing the sequence formed by these differences (the second difference) is a constant. In this case the solution is a quadratic rule. Similarly, if the third differences are the same, the rule is cubic and so on.If the question mentions geometric sequence then that shows that each term is a fixed multiple (which may be smaller than 1, or negative) of the preceding term. This is known as the "common ratio".The position to term formula for a geometric sequence is:U(n) = a + r^n for the nth term,where n is a counter that locates the term in the sequence (n = 1, 2, 3, ...)r is the common difference anda is the 0th term. That is, the term that would have come before the first term if you continued the sequence for one step in the reverse direction.Then there are special sequences that students are often expected to recognise. These include:1, 3, 6, 10, 15, ... (triangular numbers - the second differences are a constant)1, 4, 9, 16, 25, ... (square numbers - the second differences are a constant)2, 3, 5, 7, 11, 13, ... (prime numbers)1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence - defined by U(1) = 1, U(2) = 1 and U(n) = U(n-2)+U(n-1) for all n >2.)
Is the second and the fourth finger has the same length?
Yes, the second and the fourth finger are the same length.
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 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 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 second difference in math?
The expression comes from sequences. Given a sequence U1, U2, U3, ... the first differences are (U2 - U1), (U3 - U2), (U4 - U3) and so on.If you consider these as the sequence V1, V2, v3, ... then the second differences in U are the first differences in V. So the second diffs are:V2 - V1 = (U3 - U2) - (U2 - U1) = U3 - 2*U2 + U1V3 - V2 = (U4 - U3) - (U3 - U2) = U4 - 2*U3 + U2, and so on.
What is the next number 20 19 17 14 in this sequence?
The next number is the sequence is 10. To find the second number, 1 was subtracted from the first number To find the third number, 2 was subtracted from the second number To find the fourth number, 3 was subtracted from the third number Therefore to find the fifth number, 4 must be subtracted from the fourth number. 14 - 4 = 10
How do you solve the formula of a sequence of numbers.?
It is impossible to "solve" the formula since you will be given only a finite number of values. If you are given k values then there is a polynomial of order (k-1) that will generate those values, and infinitely more polynomials of higher order which will do so. Furthermore, there are non-polynomial functions that will do the trick as well.Having said that, there are some things you can do towards solving the formula. The question is usually answered using Occam's razor: if there are two or more possible solutions, use the simpler one.If the question mentions arithmetic sequence, then you know that each term in the sequence is equal to the preceding term plus some constant (which may be negative). This is known as the "common difference".The position to term formula for an arithmetic sequence is:U(n) = a + d*n for the nth term,where n is a counter that locates the term in the sequence (n = 1, 2, 3, ...)d is the common difference anda is the 0th term. That is, the term that would have come before the first term if you continued the sequence for one step in the reverse direction.There are polynomial sequences, where the first round of calculating differences between successive terms does not yield a constant but differencing the sequence formed by these differences (the second difference) is a constant. In this case the solution is a quadratic rule. Similarly, if the third differences are the same, the rule is cubic and so on.If the question mentions geometric sequence then that shows that each term is a fixed multiple (which may be smaller than 1, or negative) of the preceding term. This is known as the "common ratio".The position to term formula for a geometric sequence is:U(n) = a + r^n for the nth term,where n is a counter that locates the term in the sequence (n = 1, 2, 3, ...)r is the common difference anda is the 0th term. That is, the term that would have come before the first term if you continued the sequence for one step in the reverse direction.Then there are special sequences that students are often expected to recognise. These include:1, 3, 6, 10, 15, ... (triangular numbers - the second differences are a constant)1, 4, 9, 16, 25, ... (square numbers - the second differences are a constant)2, 3, 5, 7, 11, 13, ... (prime numbers)1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence - defined by U(1) = 1, U(2) = 1 and U(n) = U(n-2)+U(n-1) for all n >2.)
What does nth mean in math?
The term nth in math means some item in a sequence; n stands for number, so if you have a sequence with a first, second, third, fourth, fifth, sixth (etc) item, you can also talk about the nth item, which is some item at some unspecified location in this sequence.
