![]() ![]() If so, please share it with someone who can use the information. You can learn more about the difference between sequences and series here. You can learn more about increasing and decreasing sequences (and when they converge) here. You also know how to find the general formula for a quadratic sequence (the nth term formula). Now you know what a quadratic sequence is and how to identify one when you see it. However, this requires multiple steps, so it is faster to solve for a by looking at second the differences and dividing by 2, as in the method above. A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant. Note that we can also solve a system of 3 linear equations in 3 variables by using 3 distinct points in the sequence. This means that our general term (formula) for this quadratic sequence is: In other words, a linear sequence results from taking the first differences of a quadratic sequence. This sequence has a constant difference between consecutive terms. It is important to note that the first differences of a quadratic sequence form a sequence. Since -3 = b + c and b = -4, we find c = 1. Any sequence that has a common second difference is a quadratic sequence. Now, we can easily solve this system of equations with elimination by subtracting the equations: Next, we look at the first and second terms of the sequence. This tells us that we have a quadratic sequence.įirst, we divide this second difference by 2 to get 4 /2 = 2. We can see that the second differences are all the same (they have a value of 4). ![]() Rence -1 1 2 7 6 4 17 10 4 31 14 4 Table of terms, first differences, and First, we create a table of first and second differences: Term So, what is a quadratic sequence? A quadratic sequence is an ordered set with constant second differences (the first differences increase by the same value each time). Some of them are arithmetic or geometric, and some are linear or quadratic. When working with sequences of numbers, it helps to be able to recognize patterns.
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