Quadratic Sequences Write the first five terms for the following sequences according to its nth term 1)n 2 2)n ) n 2 + n 4) 2n 2 5) 2n ) 2n 2 + 3n 7) 2n 2 + 2n + 5 T1T2T3T4T

Find the nth term of a Quadratic Sequence n st Difference nd Difference222 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 2 nd difference then this would be a quadratic sequence (contains n 2 and possibily other n’s and numbers) The constant 2 tells us there is an n 2 term (square numbers are useful here). The number in front of the n 2 term is determined by dividing the constant term 2 by 2 = 1

Find the nth term of a Quadratic Sequence n st Difference nd Difference222 The constant 2 tells us there is an n 2 term (square numbers are useful here). The number in front of the n 2 term is determined by dividing the constant term 2 by 2 = n Subtract11111 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 n 2 + 1

Find the nth term of a Quadratic Sequence st Difference nd Difference222 The constant 2 tells us there is an n 2 term (square numbers are useful here). The number in front of the n 2 term is determined by dividing the constant term 2 by 2 = n Subtract33333 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 n 2 + 3

Find the nth term of a Quadratic Sequence st Difference nd Difference444 The constant 4 tells us there is an n 2 term (square numbers are useful here). The number in front of the n 2 term is determined by dividing the constant term 4 by 2 = n Subtract12345 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 termnCombine the two 2n 2 + n

Find the nth term of a Quadratic Sequence st Difference nd Difference222 The constant 4 tells us there is an n 2 term (square numbers are useful here). The number in front of the n 2 term is determined by dividing the constant term 2 by 2 = n Subtract 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 term2n + 3Combine the two n 2 + 2n + 3