New SAT Math Workbook

Next in the standard equation let a 2 r 4 and n 4

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Unformatted text preview: al about the x-axis Mirror images symmetrical about the y-axis Mirror images symmetrical about the line of the equation x = y Mirror images symmetrical about the line of the equation x = –y None of the above y Not enough information to answer the question is given. www.petersons.com 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...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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