Tham khảo tài liệu 'new sat math workbook episode 2 part 5', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Numbers and Operations Algebra and Functions 245 1. SEQUENCES INVOLVING EXPONENTIAL GROWTH GEOMETRIC SEQUENCES In a sequence of terms involving exponential growth which the testing service also calls a geometric sequence there is a constant ratio between consecutive terms. In other words each successive term is the same multiple of the preceding one. For example in the sequence 2 4 8 16 32 . . . notice that you multipy each term by 2 to obtain the next term and so the constant ratio multiple is 2. To solve problems involving geometric sequence you can apply the following standard equation a r n - 1 T In this equation The variable a is the value of the first term in the sequence The variable r is the constant ratio multiple The variable n is the position number of any particular term in the sequence The variable T is the value of term n If you know the values of any three of the four variables in this standard equation then you can solve for the fourth one. On the SAT geometric sequence problems generally ask for the value of either a or T. Example solving for T when a and r are given The first term of a geometric sequence is 2 and the constant multiple is 3. Find the second third and fourth terms. Solution 2nd term T 2 3 2 - 1 2 31 6 3rd term T 2 3 3 - 1 2 32 2 9 18 4th term T 2 3 4 - 1 2 33 2 27 54 To solve for T when a and r are given as an alternative to applying the standard equation you can multiply a by r n-1 times. Given a 2 and r 3 2nd term T 2 3 6 3rd term T 2 3 6 3 18 4th term T 2 3 6 3 18 3 54 NOTE Using the alternative method you may wish to use your calculator to find T if a and or r are large numbers. Example solving for a when r and T are given The fifth term of a geometric sequence is 768 and the constant multiple is 4. Find the 1st term a . Solution a X 4 5-1 768 a X 44 768 a X 256 768 a 768 256 a 3 246 Chapter 15 Example solving for T when a and another term in the sequence are given To find a particular term T in a geometric .
