1. Sequences Learning Outcomes  I can Find the n th term for sequences.  I can use different methods to find the nth term and explore sequences  I can understand the role of counter examples in the context of rules for sequences and disproving hypotheses

2. Sequences The nth term of a sequence 1)Consider the sequence developed by linear function a)y = 2x + 1 x12345 y b) y = 3x + 1 x12345 y c) y = mx + 1 x12345 y

3. Sequences Linear functions The nth term of a sequence 1)Consider the sequence developed by linear function a)y = 2x + 1 x12345 y b) y = 3x + 1 c) y = mx + 1 ∴ with linear function the first difference is constant

4. Sequences Linear / Quadratic functions 4nnTndifference 415 829 12313 16417 20521 Linear n2n2 nTn1 st diff2 nd diff 114 427 9312 16419 25528 Quadratic Tn = 4n + 1 + 1+ 3 Tn = n 2 + 3 2nd diff = 2 → n 2 = 4 → 2n 2 = 6 → 3n 2

5. Sequences Sequences of the form an 2 + bn + c nTn1 st diff2 nd diff 16 215 328 445 566 The nth term of a sequence

6. Sequences Additional Notes

7. Sequences Learning Outcomes: At the end of the topic I will be able to Can Revise Do Further        I can Find the n th term for sequences.  I can use different methods to find the nth term and explore sequences  I can understand the role of counter examples in the context of rules for sequences and disproving hypotheses