Chapter 1 sequences and series

CHAPTER 1 SEQUENCES AND SERIES MALAYSIA INSTITUTE OF INFORMATION TECHNOLOGY UNIVERSITI KUALA LUMPUR UPDATED: JUN 2011

1.1 SEQUENCE ,[object Object],[object Object],[object Object],1 st term 2nd term 3 rd term 4 th term 5 th term 1 st term 2nd term 3 rd term 4 th term 5 th term Each no in the list is called a term . Each term are separated by commas . Finite sequence end after a certain no of terms. Infinite sequence is one that continues indefinitely (non stop). finite sequence infinite sequence

1.1.1 Finding the formula for the n th terms of a sequence ,[object Object],[object Object],[object Object],[object Object],[object Object],The formula for the terms in sequence can be given as a formula for the n th term. 2/(5 n ) 2(n)+1

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Write the first 6 terms of x(k)=2 k . Solution: The first 6 terms is 2,4,8,16,32,64

1.2 SERIES ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1 st term 2nd term 3 rd term 4 th term 5 th term 1 st term 2nd term 3 rd term 4 th term 5 th term Series is the sum of terms in a sequence. Summation notation is Finite series end after a certain no of terms. Infinite series is one that continues indefinitely (non stop). finite series infinite series Last value of r in the sequence First value of r in the sequence First value of r in the sequence Infinity

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

1. 3 ARITHMETIC SEQUENCE AND SERIES 1.3.1 ARITHMETIC SEQUENCE ,[object Object],[object Object],[object Object],[object Object],[object Object],14 -10 6 -2 10 - 6 d = 4 d = 4 d = 4

Formula for the n th term, a = the first term d = common difference Example 7: Find the tenth term of the arithmetic sequence: 32, 47, 62, 77,…..

[object Object],[object Object]

1.3.2 ARITHMETIC SERIES ,[object Object],[object Object],[object Object],[object Object]

Exercises ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Application Problems ,[object Object],[object Object]

Application Problems ,[object Object],4. A restaurant has square tables which seat four people. When two tables are placed together, six people can be seated. If 20 square tables are placed together to form one long table, how many people can be seated? If 1000 square tables are placed together to form one very long table, how many people can be seated?( 42, 2002 )

1. 4 GEOMETRIC SEQUENCE AND SERIES 1.4.1 GEOMETRIC SEQUENCE ,[object Object],[object Object],[object Object],[object Object],[object Object],-8/4 16/-8 -32/16 r = -2 r = -2 r = -2

Formula for the n th term, a = the first term r = common ratio Example 11: Determine the eighth term of the geometric sequence: 4, 12, 36,108,…..

1.4.2 GEOMETRIC SERIES ,[object Object],[object Object],[object Object],[object Object],[object Object]

Exercises ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solution Exercise No 4 ,[object Object],Step 1: Step 2: Step 3:

Solution Exercise No 6 ,[object Object],Step 1: Step 2: Step 3: Step 4:

Application problems ,[object Object],[object Object]

Chapter 1 sequences and series

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Chapter 1 sequences and series