2. Arithmetic Sequence Aims: To know the nth term rule for an arithmetic Sequence. Be able to find the nth term of an arithmetic Sequence given sufficient information.

3. Lesson Outcomes Name: Know what an arithmetic sequence is. Describe: The nth term rule of an arithmetic sequence and what you need to write it down. Explain: How to use other information and/or simultaneous equations to find the nth term rule.

4. Maths 2C p257-258 Q1,2,3,6 Next Lesson: Arithmetic Series. Summing the terms of arithmetic sequences. Bhāskara II: 12 th Century Indian Mathematician who wrote Lilavati a text containing some of the earliest work on arithmetic (and geometric) sequences.

5. An “Arithmetic Sequence”......is a sequence which increases or decreses by the same value (d) between each term, with a starting term (a). E.g. 3,5,7,9,11... The terms are... Recursive Definition u n+1 =u n +d u 1 =a nth term u r =a+(n-1)d unun u1u1 u2u2 u3u3 u4u4 u5u5 Termaa+da+2da+3da+4d

6. Finding The nth term The nth term rule u n =a+(n-1)d We need to know a and d so lets find the nth term for these arithmetic sequences... 3,7,...,15,...,23 5,...,...,14......,...,4,...,...,...,16 5 th term 9, 100 th term 199

7. Find the nth term rule First Term 8 and Common Difference 6 u n = 8+(n-1)6 = 8+6(n-1)

8. Find the nth term rule First Term -9 and Common Difference 7 u n = -9+(n-1)7 = -9 + 7(n-1)

9. Find the nth term rule First Term 5 and Common Difference -8 u n = 5+(n-1)(-8) = 5-8(n-1)

10. Find the nth term rule First Term 0 and Common Difference -9 u n = 0+(n-1)(-9) = 0-(n-1)9 =-9(n-1)

11. Find the nth term rule 7 14 21 28 35 u n = 7 + (n-1)(7) = 7n

12. Find the nth term rule 3 13 23 33 43 u n = 3 + (n-1)(10) = 3 + 10(n-1)

13. Find the nth term rule 8 11 14 17 20 u n = 8 + (n-1)(3) = 8 + 3(n-1)

14. Find the nth term rule 7 2 -3 -8 -13 u n = 7 + (n-1)(-5) = 7 – 5(n-1)

15. Find the nth term rule 4 13 22 31 40 u n = 4 + (n-1)(9) = 4 + 9(n-1)

16. Find the nth term rule u 22 = 175 and u 28 = 223 u n = 7 + (n-1)(8) = 7 + 8(n-1)

17. Find the nth term rule u 1 = 2 and u 39 = 268 u n = 2 + (n-1)(7) = 2 + 7(n-1)

18. Find the nth term rule u 100 = 801 and u 73 = 585 u n = 9 + (n-1)(8) = 9 + 8(n-1)

19. Find the nth term rule u 32 = 147 and u 35 = 162 u n = -8 + 5(n-1)

20. Find the nth term rule u 35 = -70 and u 95 = -190 u n = -2 -2(n-1) = -2n

21. Find the nth term rule u 45 = -268 and u 88 = -526 u n = -4 + (n-1)(-6) = -4 – 6(n-1)

22. How Many Terms (what is n?) How many terms are in the sequence 4, 11, 18, 25, …, 557 80

23. How Many Terms (what is n?) How many terms are in the sequence 3, 14, 25, 36, …, 410 38

24. How Many Terms (what is n?) How many terms are in the sequence 7, 13, 19, 25, …, 241 40

25. Simultaneous Again! An arithmetic sequence has a third term that is three times the first and double the second. If the common difference is 8 find the nth term rule.

26. Trickier Simultaneous The first three terms of an arithmetic progression are… t, 2t + 2 and 4t – 2 respectively. Find the value of t and hence write down the nth term rule.

27. Special Sequences Triangle Numbers Factorial Sequence Pascal’s Triangle loads of sequences!