数学--Chapter-2--Arithmetic-Sequence.ppt

Mathematics SLChapter 2Arithmetic Sequences Sophia Zheng.Topicsqvocabularyqdefinitionqgerneral term fomulaqarithmetic mean（middle term）2.Vocabularyuarithmetic sequenceuprevious termufixed numberuconstantucommom differenceuconsecutive termsuarithmetic mean3.DefinitionReview Number sequence:A number sequence is a set of numbers defined by a rule for positive integers.PreviewArithmetic sequenceI.An arithmetic sequence is a sequence in which each term differs from the previous one by the same fixed number.II.unis arithmetic un+1-un=d for all positive integers n where d is a constant(the common difference).4.Gerneral Term Fomula The general term(or nth term)is the first termcommon difference the mth termcommon difference5.Arithmetic MeanIf a,b,c are any consecutive terms of an arithmetic sequence,then the arithmetic mean of a and c is b,where 6.Example 1A sequence is defined by I.Prove that the sequence is arithmeticII.Find and .III.Find the 57th term.IV.What is the least term of the sequence which is greater than 450?7.Example 2If are three consecutive terms of an arithmetic sequence,find the integer x.8.Example 3Find the general term for an arithmetic sequence given that 9.Exercise 1.A sequence is defined by I.Prove that the sequence is arithmetic.II.Find and .III.Find u75IV.For what values of n are the terms of the sequence less than-200?2.Find k given the consecutive arithmetic terms:k,k2,k2+6.I.II.3.Find the general term for an arithmetic sequence given that:the eleventh and eighth terms are-16 and-11.5 respectively.10.Summary vocabularykey pointstwo definitions:unis arithmetic un+1-un=d middle termtwo formulas:11.THE ENDTHE END12.