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THE FIRST OF THE POWER SEQUENCES!

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A sequence in which a constant (d) is determined on the second level D 2 of subtracting is called a Quadratic Sequence. The constant (d) that occurs at level D2 is called the Common Difference. To find the common difference (d), subtract any term by the one that proceeds it. Continue each level until you discover a common difference. 1 4 9 16 25 3 57 9 t1t1 t2t2 t3t3 t4t4 t5t5 222 D1D1 D2D2

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Find the common difference of each sequence and indicate at which level (d) was found. 1. 6, 12, 22, 36, 54, … 2. 1, -5, -15, -29, -47, …. 6 10 14 18 4 4 4 d = 4 at level D2D2 -6 -10 -14 -18 -4 d = at level D2D2

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Now you try! Find the first term and the common difference of each of these quadratic sequences. b) 1, -2, -9, -20, …. a) 3, 12, 27, 48, …. d) 3, 6, 13, 24, … c) 5, 8, 13. 20, …

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b) 1, -2, -9, -20, …. a) 3, 12, 27, 48, …. d) 3, 6, 13, 24, … c) 5, 8, 13. 20, … Answers with solutions a = 3 and d 2 = 6 on Level D2 a = 1 and d 2 = -4 on Level D2 a = 5 and d 2 = 2 on Level D2 a = 3 and d 2 = 4 on Level D2

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A Quadratic Sequence is a sequence of numbers or terms where the common difference occurs at D2. What about a sequence of numbers or terms where the common difference occurs at D3?, at D4? At D5? Find the common difference and at which level it occurs for the following sequences? a) 1, 2, 7, 6, 29, ….. b)6, 21, 86, 261, 630, ….. c) 0, -12, -48, -120, -240, ….. d) -4, -2, 8, 26, 52, …..

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Each of these sequences is a member of the Power Sequences. If the common difference occurs at Level D2, the sequence is Quadratic! If the common difference occurs at level D3, the sequence is Cubic! If the common difference occurs at level D4, the sequence is Quartic! Level D2 Quadratic Sequence Level D3 Cubic Sequence Level D4 Quartic Sequence

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