SEQUENCES. Introduction The symbols and words of Sequences......... n is a symbol used all the time in sequences n simply represents a counting number.

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Presentation transcript:

SEQUENCES

Introduction The symbols and words of Sequences n is a symbol used all the time in sequences n simply represents a counting number set to 1,2,3,4,5.... n = 1 then 2 then 3 then 4 then 5.. We use the word “term” and with n say the “nth term” of a sequence

Simple Sequences A sequence is a list of numbers obtained by a rule )3, 6, 9, 12, 15, Did you recognise this list as the 3 x table ? Sequence = 3n 2)4, 7, 10, 13, 16, Did you recognise this as 3n with 1 added ? Sequence = 3n + 1 3)1, 4, 7, 10, 13, What sequence ? 4)5, 9, 13, 17, 21, What sequence ? 5)8, 14, 20, 26, 32, What sequence ?

Simple Sequences A sequence is a list of numbers obtained by a rule )3, 6, 9, 12, 15, Did you recognise this list as the 3 x table ? Sequence = 3n 2)4, 7, 10, 13, 16, Did you recognise this as 3n with 1 added ? Sequence = 3n + 1 3)1, 4, 7, 10, 13, Sequence = 3n - 2 4)5, 9, 13, 17, 21, Sequence = 4n + 1 5)8, 14, 20, 26, 32, 38.. Sequence = 6n + 2

A Closer Look.... Lets look at defining sequences in greater detail 4, 9, 14, 19, 24, 29, Common Difference between each term ? 5 So the sequence is based on 5n ! Is it 5n exactly ? No ! So make an adjustment Compare 4, 9, 14, 19.. with 5, 10, 15, 20.. Sequence = 5n – 1 lets do another.....

Another Example... 9, 16, 23, 30, 37, 44, 51, Common Difference =

Another Example... 9, 16, 23, 30, 37, 44, 51, Common Difference = 7 So sequence is based on ?

Another Example... 9, 16, 23, 30, 37, 44, 51, Common Difference = 7 So sequence is based on 7n Is it exactly 7n ? No ! Make the necessary adjustment

Another Example... 9, 16, 23, 30, 37, 44, 51, Common Difference = 7 So sequence is based on 7n Is it exactly 7n ? Make the necessary adjustment add 2 Sequence = 7n + 2 Time for you to do an practice exercise

Practise Exercise 1)3, 7, 11, 15, 19, 23,.. 2)5, 13, 21, 29, 37, )13, 22, 31, 40, 49,... 4)17, 31, 45, 59, 63,...

Practise Exercise 1)3, 7, 11, 15, 19, 23,.. Common Difference = 4, 4n - 1 2) 5, 13, 21, 29, 37,..... Common Difference = 8, 8n - 3 3) 13, 22, 31, 40, 49,... Common Difference = 9, 9n + 4 4) 17, 31, 45, 59, 63,... Common Difference = 14, 14n + 3

Extension Exercise 1)3, 7, 11, 15, 19, 23,.. Find the 20 th term 4n - 1 (4x20) – 1 = 79 2) 5, 13, 21, 29, 37,..... Find the 14 th term 8n – 3 (8x14) – 3 = 109 3) 13, 22, 31, 40, 49,... Find the 12 th term 9n + 4 (9x12) + 4 = 112 4) 17, 31, 45, 59, 63,... Find the 51 st term 14n + 3 (14x51) + 3 = 717

SUMMARY Sequences are lists of numbers generated from a rule or formula e.g 5n, 12n The symbol n is used to represent a counting number n = 1, 2, 3, 4, etc We have studied sequences with Common Differences – we shall study others later.... SUMMARY Sequences are lists of numbers generated from a rule or formula e.g 5n, 12n The symbol n is used to represent a counting number n = 1, 2, 3, 4, etc We have studied sequences with Common Differences – we shall study others later....