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What is the formula for the nth term of a quadratic sequence?
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A quadratic sequence is a sequence of numbers in which each term is generated by a quadratic function. The formula for the nth term of a quadratic sequence is:

$a_n = a_1 + (n-1)d + \frac{(n-1)(n-2)r}{2}$

Where:

$a_1$ is the first term of the sequence $d$ is the common difference between consecutive terms $r$ is the common ratio between consecutive terms

For example, if the first term of a quadratic sequence is 2, the common difference is 3 and the common ratio is 4, the quadratic sequence is: $2,5,14,30,62,126...$

The nth term of this sequence can be found by plugging the values into the formula: $a_n = 2 + (n-1)3 + \frac{(n-1)(n-2)4}{2}$

So, the fifth term of this sequence is 30, the 8th term is 126 and so on.

It's also possible to write the nth term of a quadratic sequence using a quadratic function, for example: $a_n = a + (n-1)b + \frac{(n-1)(n-2)c}{2}$ where $a, b, c$ are the constant coefficients of the quadratic function.

by Platinum (102k points)

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