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Quadratic Sequences

Quadratic Sequences Write the first five terms for the following sequences according to its nth term 1) n 2 2) n 2 + 1 3) n 2 + n 4) 2n 2 5) 2n 2 + 4 6) 2n 2 + 3n 7) 2n 2 + 2n + 5. T1 T2 T3 T4 T5. 1 4 9 16 25. 2 5 10 17 26. 3 6 12 20 30. 2 8 18 32 50. 6 12 22 36 54.

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Quadratic Sequences

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  1. Quadratic Sequences Write the first five terms for the following sequences according to its nth term 1) n2 2) n2 + 1 3) n2 + n 4) 2n2 5) 2n2 + 4 6) 2n2 + 3n 7) 2n2 + 2n + 5 T1 T2 T3 T4 T5 1 4 9 16 25 2 5 10 17 26 3 6 12 20 30 2 8 18 32 50 6 12 22 36 54 5 14 27 44 65 9 17 29 45 65

  2. Find the nth term of a Quadratic Sequence n2 + 1 2 5 10 17 26 1st Difference 3 5 7 9 2nd Difference 2 2 2 If there is a constant 1st difference then this would be a linear sequence (contains just n’s and numbers) If there is a constant 2nd difference then this would be a quadratic sequence (contains n2 and possibily other n’s and numbers) The constant 2 tells us there is an n2 term (square numbers are useful here). The number in front of the n2 term is determined by dividing the constant term 2 by 2 = 1

  3. Find the nth term of a Quadratic Sequence n2 + 1 2 5 10 17 26 1st Difference 3 5 7 9 2nd Difference 2 2 2 The constant 2 tells us there is an n2 term (square numbers are useful here). The number in front of the n2 term is determined by dividing the constant term 2 by 2 = 1 2 5 10 17 26 n2 1 4 9 16 25 Subtract 1 1 1 1 1 This final sequence can be described as just 1, it doesn’t matter what n is, each term is just 1 Thus combine the two parts n2 + 1

  4. Find the nth term of a Quadratic Sequence 4 7 12 19 28 1st Difference 3 5 7 9 2nd Difference 2 2 2 The constant 2 tells us there is an n2 term (square numbers are useful here). The number in front of the n2 term is determined by dividing the constant term 2 by 2 = 1 4 7 12 19 28 n2 1 4 9 16 25 Subtract 3 3 3 3 3 This final sequence can be described as just 3, it doesn’t matter what n is, each term is just 3 Thus combine the two parts n2 + 3

  5. Find the nth term of a Quadratic Sequence 3 10 21 36 55 1st Difference 7 11 15 19 2nd Difference 4 4 4 The constant 4 tells us there is an n2 term (square numbers are useful here). The number in front of the n2 term is determined by dividing the constant term 4 by 2 = 2 3 10 21 36 55 2n2 2 8 18 32 50 Subtract 1 2 3 4 5 This final sequence is not constant but it is linear, just n’s and numbers. How would you describe this sequence by itself? Difference x n + zero term n Combine the two 2n2 + n

  6. Find the nth term of a Quadratic Sequence 6 11 18 27 38 1st Difference 5 7 9 11 2nd Difference 2 2 2 The constant 4 tells us there is an n2 term (square numbers are useful here). The number in front of the n2 term is determined by dividing the constant term 2 by 2 = 1 6 11 18 27 38 n2 1 4 9 16 25 Subtract 5 7 9 11 13 This final sequence is not constant but it is linear, just n’s and numbers. How would you describe this sequence by itself? Difference x n + zero term 2n + 3 Combine the two n2 + 2n + 3

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