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. Substituting the value of r, we get, Therefore, the recursive formula is. The formula to find the recursive formula for the geometric sequence is given by. Now, we shall determine the recursive formula for this geometric sequence. In order to find the fifth term, for example, we need to plug n 5. ![]() This formula allows us to simply plug in the number of the term we are interested in, and we will get the value of that term. a ( n) 3 + 2 ( n 1) In the formula, n is any term number and a ( n) is the n th term. This gives us any number we want in the series. Also, And, Hence, dividing each term of the sequence, the common ratio is. Here is an explicit formula of the sequence 3, 5, 7. ![]() 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. ![]() Top answer: To find the second term of the sequence, we need to substitute n 2 into the. Given the recursive formula for the geometric sequence a1 5, a n 2/5 a n-1, find the second term of the 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. Top answer: The second term of the sequence is given by the formula an 25an-1.
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