Maybe these having two levels of numbers to calculate the current number would imply that it would be some kind of quadratic function just as if I only had 1 level, it would be linear which is easier to calculate by hand. As with any recursive formula, the initial term must be given. Then each term is nine times the previous term. For example, suppose the common ratio is 9. Each term is the product of the common ratio and the previous term. This gives us any number we want in the series. A recursive formula allows us to find any term of a geometric sequence by using the previous term. For the following exercises, write a recursive formula for each arithmetic sequence. I do not know any good way to find out what the quadratic might be without doing a quadratic regression in the calculator, in the TI series, this is known as STAT, so plugging the original numbers in, I ended with the equation:į(x) = 17.5x^2 - 27.5x + 15. For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence. Then the second difference (60 - 25 = 35, 95-60 = 35, 130-95=35, 165-130 = 35) gives a second common difference, so we know that it is quadratic. License Terms: IMathAS Community License CC-BY + GPL
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