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LHS CAT4e ISM-11-final

LHS CAT4e ISM-11-final - Chapter 11 FURTHER TOPICS IN...

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1086 Chapter 11 FURTHER TOPICS IN ALGEBRA Section 11.1: Sequences and Series Connections (page 998) 1. After the first two terms, each of which is 1, the terms of the sequence are found by adding the two preceding terms. Thus, the third term is 1 1 2, + = the fourth is 1 2 3, + = and so on. 2. (Assume the original male honeybee is in generation 1.) 1 2 1 2 1 1 , if 3 n n n a a a a a n = = = + Exercises 1. a n 4 n 10 Replace n with 1, 2, 3, 4, and 5. n 1: a 1 4(1) 10 14 n 2: a 2 4(2) 10 18 n 3: a 3 4(3) 10 22 n 4: a 4 4(4) 10 26 n 5: a 5 4(5) 10 30 The first five terms are 14, 18, 22, 26, and 30. 2. a n 6 n 3 Replace n with 1, 2, 3, 4, and 5. n 1: a 1 6(1) 3 3 n 2: a 2 6(2) 3 9 n 3: a 3 6(3) 3 15 n 4: a 4 6(4) 3 21 n 5: a 5 6(5) 3 27 The first five terms are 3, 9, 15, 21, and 27. 3. 5 4 n n a n + = + Replace n with 1, 2, 3, 4, and 5. n 1: 1 5 6 1 1 4 5 a + + = = n 2: 2 5 7 2 2 4 6 a + + = = n 3: 3 5 8 3 3 4 7 a + + = = n 4: 4 5 9 4 4 4 8 a + + = = n 5: 5 5 10 5 5 4 9 a + + = = The first five terms are 6 7 8 9 5 6 7 8 , , , , and 10 9 . 4. 7 6 n n a n = Replace n with 1, 2, 3, 4, and 5. n 1: 1 7 6 6 1 1 6 5 5 a = = = n 2: 2 7 5 5 2 2 6 4 4 a = = = n 3: 3 7 4 4 3 3 6 3 3 a = = = n 4: 4 7 3 3 4 4 6 2 2 a = = = n 5: 5 7 2 5 5 6 1 2 a = = = The first five terms are 6 5 3 4 5 4 3 2 , , , , and 2. 5. ( ) ( ) 1 3 1 n n a n = Replace n with 1, 2, 3, 4, and 5. n 1: ( ) ( ) ( ) ( ) 1 1 1 1 3 3 1 1 0 0 a = = = n 2: ( ) ( ) ( ) ( ) 2 1 1 1 2 3 9 9 2 1 1 a = = = n 3: ( ) ( ) ( ) ( ) 3 1 1 2 3 3 27 27 3 1 2 a = = = n 4: ( ) ( ) ( ) ( ) 4 1 1 1 4 3 81 27 4 1 3 a = = = n 5: ( ) ( ) ( ) ( ) 5 1 1 4 5 3 243 243 5 1 4 a = = = The first five terms are 0, 1 2 1 4 9 27 27 243 , , ,and . 6. ( ) ( ) 2 n n a n = − Replace n with 1, 2, 3, 4, and 5. n 1: ( ) ( ) ( ) 1 1 2 1 2 1 2 a = − = − = − n 2: ( ) ( ) ( ) 2 2 2 2 4 2 8 a = − = = n 3: ( ) ( ) ( ) 3 3 2 3 8 3 24 a = − = − = − n 4: ( ) ( ) ( ) 4 4 2 4 16 4 64 a = − = = n 5: ( ) ( ) ( ) 5 5 2 5 32 5 160 a = − = − = − The first five terms are 2, 8, 24,64,and 160.

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Section 11.1: Sequences and Series 1087 7. ( ) ( ) 1 2 n n a n = − Replace n with 1, 2, 3, 4, and 5. n 1: ( ) ( ) ( ) 1 1 1 2 1 1 2 2 a = − = − = − n 2: ( ) ( ) ( ) 2 2 1 2 2 1 4 4 a = − = = n 3: ( ) ( ) ( ) 3 3 1 2 3 1 6 6 a = − = − = − n 4: ( ) ( ) ( ) 4 4 1 2 4 1 8 8 a = − = = n 5: ( ) ( ) ( ) 5 5 1 2 5 1 10 10 a = − = − = − The first five terms are 2, 4, 6, 8, and 10. 8. ( ) ( ) 1 1 1 n n a n = − + Replace n with 1, 2, 3, 4, and 5. n 1: ( ) ( ) ( ) ( ) ( ) 1 1 0 1 1 1 1 1 2 1 2 2 a = − + = − = = n 2: ( ) ( ) ( ) ( ) ( ) 2 1 1 2 1 2 1 1 3 1 3 3 a = − + = − = − = − n 3: ( ) ( ) ( ) ( ) ( ) 3 1 2 3 1 3 1 1 4 1 4 4 a = − + = − = = n 4: ( ) ( ) ( ) ( ) ( ) 4 1 3 4 1 4 1 1 5 1 5 5 a = − + = − = − = − n 5: ( ) ( ) ( ) ( ) ( ) 5 1 4 5 1 5 1 1 6 1 6 6 a = − + = − = = The first five terms are 2, 3, 4, 5, and 6. 9. 2 4 1 2 n n a n = + Replace n with 1, 2, 3, 4, and 5. n 1: ( ) ( ) 1 2 4 1 1 4 1 3 1 1 2 3 1 2 a = = = = + + n 2: ( ) ( ) 2 2 4 2 1 8 1 7 4 2 6 2 2 a = = = + + n 3: ( ) ( ) 3 2 4 3 1 12 1 11 1 9 2 11 3 2 a = = = = + + n 4: ( ) ( ) 4 2 4 4 1 16 1 15 5 16 2 18 6 4 2 a = = = = + + n 5: ( ) ( ) 5 2 4 5 1 20 1 19 25 2 27 5 2 a = = = + + The first five terms are 1, 7 5 19 6 6 27 , 1, , and . 10. 2 2 1 1 n n a n = + Replace n with 1, 2, 3, 4, and 5. 2 1 2 1 1 1 1 0 1: 0 1 1 2 1 1 n a = = = = = + + 2 2 2 2 1 4 1 3 2 : 4 1 5 2 1 n a = = = = + + 2 3 2 3 1 9 1 8 4 3: 9 1 10 5 3 1 n a = = = = = + + 2 4 2 4 1 16 1 15 4 : 16 1 17 4 1 n a = = = = + + 2 5 2 5 1 25 1 24 12 5 : 25 1 26 13 5 1 n a = = = = = + + The first five terms are 3 15 4 12 5 5 17 13 0, , , , and .
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LHS CAT4e ISM-11-final - Chapter 11 FURTHER TOPICS IN...

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