Transcript SEQUENCES
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..... 1) 3, 6, 9, 12, 15, 18 ..... Did you recognise this list as the 3 x table ? Sequence = 3n 2) 4, 7, 10, 13, 16, 19 .... Did you recognise this as 3n with 1 added ? Sequence = 3n + 1 3) 1, 4, 7, 10, 13, 16 .... What sequence ? 4) 5, 9, 13, 17, 21, 25 ..... What sequence ? 5) 8, 14, 20, 26, 32, 38 ... What sequence ? Simple Sequences A sequence is a list of numbers obtained by a rule..... 1) 3, 6, 9, 12, 15, 18 ..... Did you recognise this list as the 3 x table ? Sequence = 3n 2) 4, 7, 10, 13, 16, 19 .... Did you recognise this as 3n with 1 added ? Sequence = 3n + 1 3) 1, 4, 7, 10, 13, 16 .... Sequence = 3n - 2 4) 5, 9, 13, 17, 21, 25 .... 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, 34 .... • • • • • 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, 58 .... • Common Difference = Another Example ... 9, 16, 23, 30, 37, 44, 51, 58 .... • Common Difference = 7 • So sequence is based on ? Another Example ... 9, 16, 23, 30, 37, 44, 51, 58 .... • • • • 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, 58 .... • 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, ..... 3) 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, .. 4n - 1 2) 5, 13, 21, 29, 37, ..... 8n – 3 3) 13, 22, 31, 40, 49, ... 9n + 4 4) 17, 31, 45, 59, 63, ... 14n + 3 Find the 20th term (4x20) – 1 = 79 Find the 14th term (8x14) – 3 = 109 Find the 12th term (9x12) + 4 = 112 Find the 51st term (14x51) + 3 = 717 SUMMARY • Sequences are lists of numbers generated from a rule or formula e.g 5n, 12n + 2 ...... • The symbol n is used to represent a counting number n = 1, 2, 3, 4, 5 .........etc • We have studied sequences with Common Differences – we shall study others later ....