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Recusrive Formulae for Quadratic Functions
It's friday and I don't want to wait until monday to ask my teacher for help again. I forgot how to do it by the time i got home lol. At the moment, we are deriving explicit and recursive formulae from number sequences. I know how to derive explicit formulas from a quadratic sequence, but not a recursive formula. Here are the number sequences and their explicit formulas:
1, 4, 9 ...........................Explicit Formula is: "tn = n^2" or more familiar as (y = x^2)
2, 6, 12 .................................Explicit Formula is: "tn = n^2 + n" or more familiar as (y = x^2 + x)
Points for first sequence: (1,1), (2,4), (3,9) * Notice that the "y" values are the numbers in the first sequence.
Points for second sequence: (1,2), (2,6), (3,12) * Same principle applies as above.
*In case your wondering, I found the second common level difference (turned out to be 2) to find my "a" value (turned out to be one) via (d2 = 2a), and used three points three equations to find my "b" (turned out to be one) and "c" (turned out to be 0) values (y = ax^2 + bx + c).
Can anyone plz show me how to find the recursive formula for these number sequences? It would be much appreciated.
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