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. This gives us any number we want in the series. An arithmetic series is the sum of the terms of an arithmetic sequence. The general term of an arithmetic sequence can be written in terms of its first term a1, common difference d, and index n as follows: an a1 + (n 1)d. This formula states that each term of the sequence is the sum of the previous two terms. d ( n ) 5 + 16 ( n 1 ) This formula is given in the standard explicit form A + B ( n 1 ) where A is the first term and that B is the common difference. It is represented by the formula an a (n-1) + a (n-2), where a1 1 and a2 1. By substituting n and an for some elements in the sequence we get a system of equations. An arithmetic sequence is a sequence where the difference d between successive terms is constant. We are given the following explicit formula of an arithmetic sequence. The task now is to find the values of p, q and r. 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. To establish the polynomial we note that the formula will have the following form. 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. In fact, the process continues until there is a sequence of three successive slopes in R11, R12, and R13 such. We then can find the first difference (linear) which does not converge to a common number (30-5 = 25, 90-30=60, 185-90=95, 315-185=130, 480-315=165. calculation of the third slope from the last. The common ratio is obtained by dividing the current. It is represented by the formula an a1 r (n-1), where a1 is the first term of the sequence, an is the nth term of the sequence, and r is the common ratio. So we have a sequence of 5, 30, 90, 185,315, 480. A geometric sequence is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed number.
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