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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.
How do you find out the formula for a Quadratic Sequence?
A quadratic sequence is when the difference between two terms changes each step. To find the formula for a quadratic sequence, one must first find the difference between the consecutive terms. Then a second difference must be found by finding the difference between the first consecutive differences.
What is an arthimetic sequence?
It is an ordered set of numbers in which the difference between any member of the sequence (except the first) and its predecessor is a constant.
What is the nth term for 3 11 21 33 47 63?
To find the pattern in the sequence 3, 11, 21, 33, 47, 63, we first need to calculate the differences between consecutive terms: 8, 10, 12, 14, 16. We notice that the differences are increasing by 2 each time. This indicates a quadratic relationship. By finding the second differences (which are constant at 2), we can conclude that the sequence follows a quadratic equation of the form an^2 + bn + c. Therefore, the nth term for this sequence is given by the quadratic equation an^2 + bn + c, where a = 1, b = 2, and c = 0.
What is the d value of the following arithmetic sequence 16 9 2 5 12 19?
The sequence in the question is NOT an arithmetic sequence. In an arithmetic sequence the difference between each term and its predecessor (the term immediately before) is a constant - including the sign. It is not enough for the difference between two successive terms (in any order) to remain constant. In the above sequence, the difference is -7 for the first two intervals and then changes to +7.
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.
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 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 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 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 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 nth term for 4 13 28 49 76?
To find the nth term of the sequence 4, 13, 28, 49, 76, we first identify the differences between consecutive terms: 9, 15, 21, 27. The second differences, which are constant at 6 (6, 6, 6), suggest that the sequence is quadratic. The nth term can be expressed as ( an^2 + bn + c ). By solving the equations based on the first few terms, we find the nth term is ( n^2 + 3n ).
List the first eight terms of the sequence formed by finding the differences of successive terms in the Fibonacci sequence?
0,1,1,2,3,5,8,13
How do you find out the formula for a Quadratic Sequence?
A quadratic sequence is when the difference between two terms changes each step. To find the formula for a quadratic sequence, one must first find the difference between the consecutive terms. Then a second difference must be found by finding the difference between the first consecutive differences.
What is an arthimetic sequence?
It is an ordered set of numbers in which the difference between any member of the sequence (except the first) and its predecessor is a constant.
What is the nth term for the sequence -2 -8 -18 -32 -50?
To find the nth term of the sequence -2, -8, -18, -32, -50, we first observe the differences between consecutive terms: -6, -10, -14, -18. The second differences (which are constant at -4) suggest that the nth term can be represented by a quadratic function. The general form is ( a_n = An^2 + Bn + C ). Solving for coefficients A, B, and C using the first few terms gives the nth term as ( a_n = -2n^2 + n ).
What is a sequence of a story?
a sequence of a story is like what happened first, second, third etc
