LHS CAT4e ISM-11-final

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 11 2 , += the fourth is 123 , and so on. 2. (Assume the original male honeybee is in generation 1.) 1 2 12 1 1 ,if 3 nn n a a aa a n −− = = =+ Exercises 1. a n 5 4 n 1 10 Replace n with 1, 2, 3, 4, and 5. n 5 1: a 1 5 4(1) 1 10 5 14 n 5 2: a 2 5 4(2) 1 10 5 18 n 5 3: a 3 5 4(3) 1 10 5 22 n 5 4: a 4 5 4(4) 1 10 5 26 n 5 5: a 5 5 4(5) 1 10 5 30 The first five terms are 14, 18, 22, 26, and 30. 2. a n 5 6 n 2 3 Replace n with 1, 2, 3, 4, and 5. n 5 1: a 1 5 6(1) 2 3 5 3 n 5 2: a 2 5 6(2) 2 3 5 9 n 5 3: a 3 5 6(3) 2 3 5 15 n 5 4: a 4 5 6(4) 2 3 5 21 n 5 5: a 5 5 6(5) 2 3 5 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 5 1: 15 6 1 14 5 a + + == n 5 2: 25 7 2 24 6 a + + n 5 3: 35 8 3 34 7 a + + n 5 4: 45 9 4 44 8 a + + n 5 5: 55 1 0 5 54 9 a + + The first five terms are 6789 5678 ,,,, and 10 9 . 4. 7 6 n n a n = Replace n with 1, 2, 3, 4, and 5. n 5 1: 17 6 6 1 16 5 5 a = n 5 2: 27 5 5 2 26 4 4 a = n 5 3: 37 4 4 3 36 3 3 a = n 5 4: 47 3 3 4 46 2 2 a = n 5 5: 57 2 5 56 1 2 a = The first five terms are 65 3 4 5432 ,,,, a n d 2 . 5. ( ) () 1 3 1 n n an =− Replace n with 1, 2, 3, 4, and 5. n 5 1: ( ) ( ) 1 11 1 33 0 0 a = = n 5 2: ( ) ( )() 2 1 2 39 9 21 1 a = = n 5 3: ( ) ( ) 3 2 3 32 7 2 7 31 2 a = = n 5 4: ( ) ( ) 4 1 4 38 1 2 7 41 3 a n 5 5: ( ) ( ) 5 4 5 4 3 2 4 3 51 4 a = = The first five terms are 0, 12 1 4 92 72 7 2 4 3 ,,, a n d . 6. ( ) 2 n n Replace n with 1, 2, 3, 4, and 5. n 5 1: ( ) ( ) 1 1 21 2 1 2 a = − n 5 2: ( )() () 2 2 224 28 a = = n 5 3: 3 3 23 8 3 2 4 a n 5 4: 4 4 241 6 4 a = = n 5 5: 5 5 2 5 32 5 160 a The first five terms are 2, 8, 24,64,and 160.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Section 11.1: Sequences and Series 1087 7. () 12 n n an =− Replace n with 1, 2, 3, 4, and 5. n 5 1: () ( ) ( ) 1 1 1 1 2 2 a ⎡⎤ ⎣⎦ n 5 2: ( ) () () 2 2 2 1 44 a = = n 5 3: ) 3 3 3 1 6 6 a = − n 5 4: ) 4 4 4 1 88 a = = n 5 5: ) () 5 5 5 1 1 0 1 0 a The first five terms are 2 2, 4, 2 6, 8, and 2 10. 8. () ( ) 1 11 n n + Replace n with 1, 2, 3, 4, and 5. n 5 1: ( ) ( ) ( )() () 0 1 1 1 2 1 2 2 a + =− = = n 5 2: () ( )() ( ) 21 1 2 1 1 31 33 a n 5 3: ( ) 2 3 13 1 1 4 1 4 4 a = = n 5 4: ( ) 41 3 4 14 1 1 51 55 a n 5 5: ( ) 4 5 15 1 1 6 1 6 6 a = = The first five terms are 2, 2 3, 4, 2 5, and 6. 9. 2 2 n n a n = + Replace n with 1, 2, 3, 4, and 5. n 5 1: ( ) 1 2 41 1 41 3 1 12 3 a == = = + + n 5 2: ( ) 2 2 42 1 81 7 42 6 22 a = + + n 5 3: ( ) 3 2 43 1 12 1 11 1 92 1 1 32 a = = + + n 5 4: ( ) 4 2 44 1 16 1 15 5 16 2 18 6 42 a = = + + n 5 5: ( ) 5 2 45 1 20 1 19 25 2 27 52 a = + + The first five terms are 1, 75 1 9 66 2 7 ,1 , ,and . 10. 2 2 1 1 n n a n = + Replace n with 1, 2, 3, 4, and 5. 2 1 2 11110 1: 0 11 2 na −− = + + 2 2 2 21413 2: 41 5 = = + + 2 3 2 31918 4 3: 91 1 0 5 = + + 2 4 2 411 611 5 4: 16 1 17 = = + + 2 5 2 512 2 5: 25 1 26 13 = = = + + The first five terms are 5 2 5 5 17 13 0, , , , and . 11. 3 8 2 n n a n + = + Replace n with 1, 2, 3, 4, and 5. 3 1 18189 3 3 3 ++ = + 3 2 28881 6 4 4 4 = + 3 3 382 783 5 7 5 5 = = = + 3 4 486 487 2 6 6 = = = + 3 5 5 8 125 8 133 19 7 7 = = = + The first five terms are 3, 4, 7, 12, and 19. 12. 3 27 3 n n a n + = + Replace n with 1, 2, 3, 4, and 5. 3 1 72 8 7 4 + = = + 3 2 2 27 8 27 35 7 23 5 5 = = = + 3 3 4 9 6 6 = = = + 3 4 76 79 1 43 7 7 = = + 3 5 5 27 125 27 152 53 8 8 = = = + The first five terms are 7, 7, 9, 13, and 19.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/13/2010 for the course MATH MAT 123 taught by Professor Smith during the Spring '10 term at Thomas Edison State.

Page1 / 86

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online