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Do sequences with an equivalent second difference have a quadratic nth term?
Wiki User
∙ 10y ago
yes
Wiki User
∙ 10y ago
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What do you do if the second difference in a quadratic equation is 1?
The second difference of a quadratic equation being one indicates the second derivative at that point is positive. What you do from there depends on what property or transformation you're looking for with respect to the equation.
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.
Is an equation considered a standard form of quadratic equation if the first term or the quadratic term is on the second side?
No, it is not.
Why is a quadratic function called a quadratic function?
A quadratic function is a second degree polynomial, that is, is involves something raised to the power of 2, also know as squaring. Quadratus is Latin for square. Hence Quadratic.
A second-degree polynomial is a quadratic polynomial?
Yes.
What do you do if the second difference in a quadratic equation is 1?
The second difference of a quadratic equation being one indicates the second derivative at that point is positive. What you do from there depends on what property or transformation you're looking for with respect to the equation.
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.
How can you tell whether a table of values represents a quadratic function?
Unless the operands form an arithmetic sequence, it is not at all simple. That means the difference between successive points must be the same. If that is the case and the SECOND difference in the results is constant then you have a quadratic.
What is quadratic mean?
Quadratic is an adjective that is used to describe something that is related to squares. For example, the quadratic equation uses squares, or the second power, and is thus quadratic.
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.
Find the quadratic sequences nth term for these 4 sequences which are separated by the letter i iii 7 10 15 22 21 42 iii 2 9 18 29 42 57 iii 4 15 32 55 85 119 iii 5 12 27 50 81 120?
Check if the given sequences are quadratic sequences. 7 10 15 22 21 42 The first difference: 3 5 7 1 21. The second difference: 2 2 6 20. Since the second difference is not constant, then the given sequence is not a quadratic sequence. 2 9 18 29 42 57 The first difference: 7, 9, 11, 13, 15. The second difference: 2 2 2 2. Since the second difference is constant, then the given sequence is a quadratic sequence. Therefore, contains a n2 term. Let n = 1, 2, 3, 4, 5, 6, ... Now, let's refer the n2 terms as, 1, 4, 9, 16, 25, 36. As you see, the terms of the given sequence and n2 terms differ by 1, 5, 9, 13, 17, 21 which is an arithmetic sequence,say {an} with a common difference d = 4 and the first term a = 1. Thus, the nth term formula for this arithmetic sequence is an = a + (n - 1)d = 1 + 4(n - 1) = 4n - 3. Therefore, we can find any nth term of the given sequence by using the formula, nth term = n2 + 4n - 3 (check, for n = 1, 2, 3, 4, 5, 6, ... and you'll obtain the given sequence) 4 15 32 55 85 119 The first difference: 11, 17, 23, 30, 34. The second difference: 6 6 7 4. Since the second difference is not constant, then the given sequence is not a quadratic sequence. 5 12 27 50 81 120 The first difference: 7, 15, 23, 31, 39. The second difference: 8 8 8 8. Since the second difference is constant, then the given sequence is a quadratic sequence. I tried to refer the square terms of sequences such as n2, 2n2, 3n2, but they didn't work, because when I subtracted their terms from the terms of the original sequence I couldn't find a common difference among the terms of those resulted sequences. But, 4n2 works. Let n = 1, 2, 3, 4, 5, 6, ... Now, let's refer the 4n2 terms as, 4, 16, 36, 64, 100, 144. As you see, the terms of the given sequence and 4n2 terms differ by 1, -4, -9, -14, -19, -24 which is an arithmetic sequence, say {an} with a common difference d = -5 and the first term a = 1. Thus, the nth term formula for this arithmetic sequence is an = a + (n - 1)d = 1 -5(n - 1) = -5n + 6. Therefore, we can find any nth term of the given sequence by using the formula, nth term = 4n2 - 5n + 6 (check, for n = 1, 2, 3, 4, 5, 6, ... and you'll obtain the given sequence)
What is the difference between quadratic function and quadratic formula?
A quadratic function is a function where a variable is raised to the second degree (2). Examples would be x2, or for more complexity, 2x2+4x+16. The quadratic formula is a way of finding the roots of a quadratic function, or where the parabola crosses the x-axis. There are many ways of finding roots, but the quadratic formula will always work for any quadratic function. In the form ax2+bx+c, the Quadratic Formula looks like this: x=-b±√b2-4ac _________ 2a The plus-minus means that there can 2 solutions.
What are the degrees of quadratic equations?
A quadratic equations have a second degrees, such that Ax^2 + Bx + C = 0
Is an equation considered a standard form of quadratic equation if the first term or the quadratic term is on the second side?
No, it is not.
Why is a quadratic function called a quadratic function?
A quadratic function is a second degree polynomial, that is, is involves something raised to the power of 2, also know as squaring. Quadratus is Latin for square. Hence Quadratic.
Is a quadratic polynomial a second-degree polynomial?
Yes.
A second-degree polynomial is a quadratic polynomial?
Yes.
