1、SEQUENCES,A sequence is a set of terms, in a definite order, where the terms are obtained by some rule.,A finite sequence ends after a certain number of terms.,An infinite sequence is one that continues indefinitely.,For example:,1, 3, 5, 7, (This is a sequence of odd numbers),1st term = 2 x 1 1 = 1
2、,2nd term = 2 x 2 1 = 3,3rd term = 2 x 3 1 = 5,nth term = 2 x n 1 = 2n - 1,. . . .,+ 2,+ 2,NOTATION,1st term = u,2nd term = u,3rd term = u,nth term = u,. . . . . .,1,2,3,n,OR,1st term = u,2nd term = u,3rd term = u,nth term = u,. . . . . .,0,1,2,n-1,FINDING THE FORMULA FOR THE TERMS OF A SEQUENCE,A r
3、ecurrence relation defines the first term(s) in the sequence and the relation between successive terms.,u = 5,u = u +3 = 8,u = u +3 = 11,u = u +3 = 3n + 2,. . .,1,2,3,n+1,For example:,5, 8, 11, 14, ,1,2,n,What to look for when looking for the rule defining a sequence,Constant difference: coefficient
4、 of n is the difference 2nd level difference: compare with square numbers(n = 1, 4, 9, 16, ) 3rd level difference: compare with cube numbers(n = 1, 8, 27, 64, ) None of these helpful: look for powers of numbers(2 = 1, 2, 4, 8, ) Signs alternate: use (-1) and (-1)-1 when k is odd +1 when k is even,k,
5、k,2,3,n - 1,EXAMPLE: Find the next three terms in the sequence 5, 8, 11, 14, ,EXAMPLE: The nth term of a sequence is given by x =Find the first four terms of the sequence.b) Which term in the sequence is ?c) Express the sequence as a recurrence relation.,1,_,2,n,n,1,1024,_,EXAMPLE: Find the nth term
6、 of the sequence +1, -4, +9, -16, +25, ,EXAMPLE: A sequence is defined by a recurrence relation of the form: M = aM + b. Given that M = 10, M = 20, M = 24, find the value of a and the value of b and hence find M .,n + 1,1,3,2,4,This powerpoint was kindly donated to http:/ is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.,
