1. 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 T1T2T3T4T5 1491625 25101726 36122030 612223654 917294565 28183250 514274465

2. Find the nth term of a Quadratic Sequence n 2 + 1 25101726 1 st Difference 3 5 7 9 2 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

3. Find the nth term of a Quadratic Sequence n 2 + 1 25101726 1 st Difference 3 5 7 9 2 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 = 1 25101726 n 2 1491625 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

4. Find the nth term of a Quadratic Sequence 47121928 1 st Difference 3 5 7 9 2 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 = 1 47121928 n 2 1491625 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

5. Find the nth term of a Quadratic Sequence 310213655 1 st Difference 7 11 15 19 2 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 = 2 310213655 2n 2 28183250 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

6. Find the nth term of a Quadratic Sequence 611182738 1 st Difference 5 7 9 11 2 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 = 1 611182738 n 2 1491625 Subtract5791113 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