Study Guide and Intervention

Transcription

1 0-7 Study Guide and Intervention A geometric sequence is a sequence in which each term after the nonzero first term is found by multiplying the previous term by a constant called the common ratio. Geometric a sequence of numbers of the form a, ar, ar 2, ar 3,, Example:, 2, 4, 8, 6, Sequence where a 0, and r 0 or Example Example 2 a. 3, 6, 9, 2, 5, In this sequence, each term is found by adding 3 to the previous term. The sequence is arithmetic and not geometric. b., 4, 6, 64, In this sequence, each term is found by multiplying the previous term by 4. The sequence is geometric. a. 8, 4, 2,, b. 7, 4, 28, 56, 4 4 The common factor is or. Use this The common ratio is or 2. Use this information to find the next three terms. information to find the next three terms. ( ) 56(2) (2) (2) The next three terms are 2, 224, The next three terms are,, and Lesson 0-7 Exercises 224(2) 448 The next three terms are 2, 224, , 4, 6, 8, 0, 2. 2, 4, 8, 6, 32, 3. 0, 5, 2.5,.25, 4. 00, 400, 600, 6400, 5.,,,, 6.,,,, , 300, 900, 2700, 8.,,,, 9. 80, 40, 20, 0, Glencoe/McGraw-Hill 65 Glencoe Algebra

2 0-7 Geometric Means A missing term or terms between two nonconsecutive terms in a geometric sequence are called geometric means. In the sequence 0, 20, 40, 80,, the geometric mean between 0 and 40 is 20. You can use the formula a n a r n to find a geometric mean. Example Study Guide and Intervention (continued) Find the geometric mean in the sequence 6,, 50. In the sequence, a = 6 and a 3 = 50. To find a 2, you must first find r. a n a r n Formula for the nth term of a geometric sequence a 3 a r 3 n r 2 a 3 50 and a r 2 6 Divide each side by r 2 Simplify. 5 r Take the square root of each side. If r 5, the geometric mean is 6(5) or 30. If r 5, the geometric mean is 6( 5) or 30. Therefore the geometric mean is 30 or 30. Exercises. 4,, ,, ,, ,, ,, ,, ,, 8.,, 9.,, ,,.,, 0 2.,, ,, ,, ,, ,, 7. 5,, 8. 8,, 320, Glencoe/McGraw-Hill 66 Glencoe Algebra

3 0-7 Skills Practice. 9, 7, 25, 33, 2. 4, 2, 36, 08, , 80, 20, 5, 4. 75, 60, 45, 30, 5. 64, 32, 6, 8, , 2, 5.5, 0, 7. 2, 4, 8, 6, 8. 2, 6, 8, 54, Lesson , 480, 240, 20, , 2430, 80, 270,. 32, 6, 8, 4, , 536, 384, 96, Find the nth term of each geometric sequence. 3. a 2, n 4, r 2 4. a 3, n 5, r 2 5. a 6, n 3, r 8 6. a 5, n 4, r 9 7. a 0, n 3, r 2 8. a 4, n 4, r ,, ,, ,, ,, ,, ,, 24 Glencoe/McGraw-Hill 67 Glencoe Algebra

4 0-7 Practice. 3, 2, 48, 92, 2. 2, 7, 32, 47, , 35, 70, 5, , 0, 55, 27.5, , 248, 62, 5.5, 6. 20, 50, 25, 32.5, 7. 4, 20, 00, 500, 8. 7, 2, 63, 89, , 250, 250, , 70, 98, 37.2, 2. 5, 4, 3.2, ,,,, Find the nth term of each geometric sequence. 3. a 6, n 5, r 3 4. a 9, n 6, r 2 5. a 8, n 3, r 6. a 50, n 7, r 3 7. a 5, n 3, r.5 8. a 7, n 5, r ,, ,, ,, ,, ,, 24.,, MAGAZINE SUBSCRIPTIONS For Exercises 25 and 26, use the following information. The manager of a teen magazine wants to increase subscriptions by at least 6% each year for the next three years to keep the company operating at a profit. Subscriptions for 2003 are 7, Determine the minimum number of subscriptions the sales team must sell for the years 2004, 2005, and Suppose the manager wants to increase the subscriptions to 35,000. How long will it take to reach this goal if subscriptions increase at 6% per year? Glencoe/McGraw-Hill 68 Glencoe Algebra

5 0-7 Reading to Learn Mathematics Pre-Activity How can a geometric sequence be used to describe a bungee jump? Read the introduction to Lesson 0-7 at the top of page 567 in your textbook. How can you find the distance of the fifth bounce? Reading the Lesson. Suppose you are given the first three terms of a geometric sequence and want to find the next three terms. a. What should you do to find the common ratio? Lesson 0-7 b. What should you do after you find the common ratio? 2. Suppose you are asked to give an example of a geometric sequence. Are there any restrictions on the terms of the sequence or the common ratio r? Explain. 3. You can use the formula for the nth term of a geometric sequence to find any term in the sequence.what information do you need in order to use the formula? 4. Consider the geometric sequence 3, 6, 2, 24, 48,. How many geometric means are there for each pair of terms? What are they? a. 3 and 2 b. 3 and 24 Helping You Remember 5. To remember an idea, it can help if you explain it to someone else. Suppose a friend thinks that the formula for the nth term of a geometric sequence should be a n a r n rather than a n a r n. How would you explain why it should be a n a r n? Glencoe/McGraw-Hill 69 Glencoe Algebra