Presentation on theme: "THE FIRST OF THE POWER SEQUENCES!"— Presentation transcript:
1 THE FIRST OF THE POWER SEQUENCES! Quadratric SequencesTHE FIRST OF THE POWER SEQUENCES!
2 Definition Quadratic Sequence. Common Difference. A sequence in which a constant (d) is determined on the second level D2 of subtracting is called aQuadratic Sequence.The constant (d) that occurs at level D2 is called theCommon 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.Definitiont1t2t3t4t5D15739D2222
3 Find the common difference of each sequence and indicate at which level (d) was found. Examples:, 12, 22, 36, 54, …d = 4 at level D2, -5, , -29, , ….d = at level D2
4 Now you try!Find the first term and the common difference of each of these quadratic sequences.a) 3, 12, 27, 48, ….b) 1, -2, -9, -20, ….c) 5, 8, , …d) 3, 6, 13, 24, …
5 Answers with solutions a = andd 2 = 6 on Level D2b) 1, -2, -9, -20, ….a = andd 2 = -4 on Level D2a = andd 2 = 2 on Level D2c) 5, 8, , …a = andd 2 = 4 on Level D2d) 3, 6, 13, 24, …
6 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, …..6, 21, 86, 261, 630 , …..c) 0, -12, -48, , , …..d) -4, -2, 8, 26, 52, …..
7 Each of these sequences is a member of the Power Sequences 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 SequenceLevel D3 Cubic SequenceLevel D4 Quartic Sequence
Your consent to our cookies if you continue to use this website.