New SAT Math Workbook

# On the new sat a problem involving either the union

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Unformatted text preview: 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 × 4 (5−1) = 768 a × 4 4 = 768 a × 256 = 768 a = 768 256 a=3 www.petersons.com 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 sequence when the first term and another term are given, first determine the constant ratio (r), and then solve for T. For example, assume that the first and sixth terms of a geometric sequence are 2 and 2048, respectively. To find the value of the fourth term, first apply the standard equation to determine r : Solution: 2 × r (6−1) = 2048 2 × r 5 = 2048 r 5 = 2048 2 5 r = 1024 r = 5 1024 r=4 The constant ratio is 4. Next, in the standard equation, let a = 2, r = 4, and n = 4, and then solve for T : 2 × 4 ( 4−1) = T 2 × 43 = T 2 × 64 = T 128 = T The fourth term in the sequence is 128. Exercise 1 Work out each problem. For questions 1–3, circle the letter that appears before your answer. Questions 4 and 5 are grid-in questions. 1. On January 1, 1950, a farmer bought a certain parcel of land for \$1,500. Since then, the land has doubled in value every 12 years. At this rate, what will the value of the land be on January 1, 2010? (A) \$7,500 (B) \$9,000 (C) \$16,000 (D) \$24,000 (E) \$48,000 A certain type of cancer cell divides into two cells every four seconds. How many cells are observable 32 seconds after observing a total of four cells? (A) 1,024 (B) 2,048 (C) 4,096 (D) 5,512 (E) 8,192 The seventh term of a geometric sequence with constant ratio 2 is 448. What is the first term of the sequence? (A) 6 (B) 7 (C) 8 (D) 9 (E) 11 4. Three years after an art collector purchases a certain painting, the value of the painting is \$2,700. If the painting increased in value by an average of 50 percent per year over the three year period, how much did the collector pay for the painting, in dollars? 2. 5. What is the second term in a geometric serie...
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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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