Finding the general term
- 2. EXAMPLE: FIND THE GENERAL TERM OF THE SEQUENCE 5, 12, 19, 26, 33, . . .
- 3. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 5 12 19 26 33 . . . ?
- 4. GET THE DIFFERENCE 𝟓, 𝟏𝟐, 𝟏𝟗, 𝟐𝟔, 𝟑𝟑, … 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟕
- 5. SOLVE FOR a AND b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟓 𝑎 1 + 𝑏 = 5 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏𝟐 𝑎 2 + 𝑏 = 12 𝟐𝒂 + 𝒃 = 𝟏𝟐 𝑬𝒒. 𝟐
- 6. 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟏𝟐 𝑬𝒒. 𝟐 𝒂 = 𝟕 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟕 + 𝒃 = 𝟓 𝒃 = 𝟓 − 𝟕 𝒃 = −𝟐 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 7. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟕𝒏 − 𝟐 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 𝟓, 𝟏𝟐, 𝟏𝟗, 𝟐𝟔, 𝟑𝟑, . . . is 𝒂 𝒏 = 𝟕𝐧 − 𝟐
- 8. EXAMPLE: FIND THE GENERAL TERM OF THE SEQUENCE 7, 11, 15, 19, 23, . . .
- 9. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 7 11 15 19 23 . . . ?
- 10. GET THE DIFFERENCE 𝟕, 𝟏𝟏, 𝟏𝟓, 𝟏𝟗, 𝟐𝟑, … 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟒
- 11. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟕 𝑎 1 + 𝑏 = 7 𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏𝟏 𝑎 2 + 𝑏 = 11 𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐
- 12. 𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐 𝒂 = 𝟒 𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟒 + 𝒃 = 𝟕 𝒃 = 𝟕 − 𝟒 𝒃 = 𝟑 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 13. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟒𝒏 + 𝟑 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 𝟓, 𝟏𝟐, 𝟏𝟗, 𝟐𝟔, 𝟑𝟑, . . . is 𝒂 𝒏 = 𝟒𝐧 + 𝟑
- 14. QUIZ: 1. FIND THE GENERAL TERM OF THE SEQUENCE 1, 3, 5, 7, 9, . . . 2. FIND THE GENERAL TERM OF THE SEQUENCE -2, 1, 4, 7, 10, . . . 3. FIND THE GENERAL TERM OF THE SEQUENCE -1, 1, 3, 5, 7, 9, . . .
- 15. QUIZ: FIND THE GENERAL TERM OF THE SEQUENCE 1, 3, 5, 7, 9, . . .
- 16. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 1 3 5 7 9 . . . ?
- 17. GET THE DIFFERENCE 𝟏, 𝟑, 𝟓, 𝟕, 𝟗, … 𝒂𝒏 + 𝒃 = 𝒂 𝒏 2
- 18. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏 𝑎 1 + 𝑏 = 1 𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟑 𝑎 2 + 𝑏 = 3 𝟐𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟐
- 19. 𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟐 𝒂 = 𝟐 𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟐 + 𝒃 = 𝟏 𝒃 = 𝟏 − 𝟐 𝒃 = −𝟏 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 20. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟐𝒏 − 𝟏 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 𝟏, 𝟑, 𝟓, 𝟕, 𝟗, . . . is 𝒂 𝒏 = 𝟐𝐧 − 𝟏
- 21. QUIZ: FIND THE GENERAL TERM OF THE SEQUENCE -2, 1, 4, 7, 10, . . .
- 22. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 -2 1 4 7 10 . . . ?
- 23. GET THE DIFFERENCE −𝟐, 𝟏, 𝟒, 𝟕, 𝟏𝟎, … 𝒂𝒏 + 𝒃 = 𝒂 𝒏 3
- 24. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = −𝟐 𝑎 1 + 𝑏 = −2 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏 𝑎 2 + 𝑏 = 1 𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐
- 25. 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐 𝒂 = 𝟑 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟑 + 𝒃 = −𝟐 𝒃 = −𝟐 − 𝟑 𝒃 = −𝟓 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 26. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟑𝒏 − 𝟓 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 −𝟐, 𝟏, 𝟒, 𝟕, 𝟏𝟎, . . . is 𝒂 𝒏 = 𝟑𝐧 − 𝟓
- 27. QUIZ: FIND THE GENERAL TERM OF THE SEQUENCE -1, 1, 3, 5, 7, 9, . . .
- 28. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 -1 1 3 5 7 . . . ?
- 29. GET THE DIFFERENCE −𝟏, 𝟏, 𝟑, 𝟓, 𝟕, 𝟗, … 𝒂𝒏 + 𝒃 = 𝒂 𝒏 2
- 30. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = −𝟏 𝑎 1 + 𝑏 = −1 𝒂 + 𝒃 = −𝟏 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟏 𝑎 2 + 𝑏 = 1 𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐
- 31. 𝒂 + 𝒃 = −𝟏 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟏 𝑬𝒒. 𝟐 𝒂 = 𝟐 𝒂 + 𝒃 = −𝟏 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟐 + 𝒃 = −𝟏 𝒃 = −𝟏 − 𝟐 𝒃 = −𝟑 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 32. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟐𝒏 − 𝟑 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 −𝟏, 𝟏, 𝟑, 𝟓, 𝟕, 𝟗, . . . is 𝒂 𝒏 = 𝟐𝐧 − 𝟑
- 33. ASSIGNMENT! FIND THE GENERAL TERM OF THE FOLLOWING. 1. 3, 7, 11, 15, . . . 2. 2, 6, 10, 14, . . . 3. 5, 11, 17, 23, . . . 4. 9, 11, 13, 15, . . . 5. -2, -5, -8, -11, . . .
- 34. ASSIGNMENT: FIND THE GENERAL TERM OF THE SEQUENCE 1. 3, 7, 11, 15, . . .
- 35. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 3 7 11 15 . . . ?
- 36. GET THE DIFFERENCE 𝟑, 𝟕, 𝟏𝟏, 𝟏𝟓, … 𝒂𝒏 + 𝒃 = 𝒂 𝒏 4
- 37. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟑 𝑎 1 + 𝑏 = 3 𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟕 𝑎 2 + 𝑏 = 7 𝟐𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟐
- 38. 𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟕 𝑬𝒒. 𝟐 𝒂 = 𝟒 𝒂 + 𝒃 = 𝟑 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟒 + 𝒃 = 𝟑 𝒃 = 𝟑 − 𝟒 𝒃 = −𝟏 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 39. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟒𝒏 − 𝟏 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 𝟑, 𝟕, 𝟏𝟏, 𝟏𝟓, . . . is 𝒂 𝒏 = 𝟒𝐧 − 𝟏
- 40. ASSIGNMENT: FIND THE GENERAL TERM OF THE SEQUENCE 2. 2, 6, 10, 14, . . .
- 41. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 2 6 10 14 . . . ?
- 42. GET THE DIFFERENCE 𝟐, 𝟔, 𝟏𝟎, 𝟏𝟒, . . . 𝒂𝒏 + 𝒃 = 𝒂 𝒏 4
- 43. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟐 𝑎 1 + 𝑏 = 2 𝒂 + 𝒃 = 𝟐 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = 𝟔 𝑎 2 + 𝑏 = 6 𝟐𝒂 + 𝒃 = 𝟔 𝑬𝒒. 𝟐
- 44. 𝒂 + 𝒃 = 𝟐 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟔 𝑬𝒒. 𝟐 𝒂 = 𝟒 𝒂 + 𝒃 = 𝟐 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟒 + 𝒃 = 𝟐 𝒃 = 𝟐 − 𝟒 𝒃 = −𝟐 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 45. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟒𝒏 − 𝟐 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 𝟐, 𝟔, 𝟏𝟎, 𝟏𝟒, . . . is 𝒂 𝒏 = 𝟒𝐧 − 𝟐
- 46. ASSIGNMENT: FIND THE GENERAL TERM OF THE SEQUENCE 3. 5, 11, 17, 23, . . .
- 47. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 5 11 17 23 . . . ?
- 48. GET THE DIFFERENCE 𝟓, 𝟏𝟏, 𝟏𝟕, 𝟐𝟑, . . . 𝒂𝒏 + 𝒃 = 𝒂 𝒏 6
- 49. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟓 𝑎 1 + 𝑏 = 5 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 𝟏𝟏 𝑎 2 + 𝑏 = 11 𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐
- 50. 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐 𝒂 = 𝟔 𝒂 + 𝒃 = 𝟓 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟔 + 𝒃 = 𝟓 𝒃 = 𝟓 − 𝟔 𝒃 = −𝟏 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 51. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟔𝒏 − 𝟏 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 𝟓, 𝟏𝟏, 𝟏𝟕, 𝟐𝟑, . . . is 𝒂 𝒏 = 𝟔𝐧 − 𝟏
- 52. ASSIGNMENT: FIND THE GENERAL TERM OF THE SEQUENCE 4. 9, 11, 13, 15, . . .
- 53. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 9 11 13 15 . . . ?
- 54. GET THE DIFFERENCE 𝟗, 𝟏𝟏, 𝟏𝟑, 𝟏𝟓, . . . 𝒂𝒏 + 𝒃 = 𝒂 𝒏 2
- 55. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = 𝟗 𝑎 1 + 𝑏 = 9 𝒂 + 𝒃 = 𝟗 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 𝟏𝟏 𝑎 2 + 𝑏 = 11 𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐
- 56. 𝒂 + 𝒃 = 𝟗 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = 𝟏𝟏 𝑬𝒒. 𝟐 𝒂 = 𝟐 𝒂 + 𝒃 = 𝟗 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. 𝟔 + 𝒃 = 𝟗 𝒃 = 𝟗 − 𝟔 𝒃 = 𝟕 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 57. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝟐𝒏 + 𝟕 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 𝟗, 𝟏𝟏, 𝟏𝟑, 𝟏𝟓, . . . is 𝒂 𝒏 = 𝟐𝐧 + 𝟕
- 58. ASSIGNMENT: FIND THE GENERAL TERM OF THE SEQUENCE 5. -2, -5, -8, -11, . . .
- 59. PREPARE A TABLE n 1 2 3 4 5 . . . n 𝒂 𝒏 -2 -5 -8 -11 . . . ?
- 60. GET THE DIFFERENCE −𝟐, −𝟓, −𝟖, −𝟏𝟏, . . . 𝒂𝒏 + 𝒃 = 𝒂 𝒏 −3
- 61. SOLVE FOR a and b. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 𝑰𝒇 𝒏 = 𝟏 𝒂𝒏𝒅 𝒂 𝒏 = −𝟐 𝑎 1 + 𝑏 = −2 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏 𝑰𝒇 𝒏 = 𝟐 𝒂𝒏𝒅 𝒂 𝒏 = −𝟓 𝑎 2 + 𝑏 = −5 𝟐𝒂 + 𝒃 = −𝟓 𝑬𝒒. 𝟐
- 62. 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏 𝟐𝒂 + 𝒃 = −𝟓 𝑬𝒒. 𝟐 𝒂 = −𝟑 𝒂 + 𝒃 = −𝟐 𝑬𝒒. 𝟏 𝒔𝒖𝒃𝒔𝒕𝒊𝒕𝒖𝒕𝒆 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂. −𝟑 + 𝒃 = −𝟐 𝒃 = −𝟐 + 𝟑 𝒃 = 𝟏 SOLVE FOR a AND b. 𝑺𝒖𝒃𝒕𝒓𝒂𝒄𝒕 𝑬𝒒. 𝟏 𝒇𝒓𝒐𝒎 𝑬𝒒. 𝟐
- 63. 𝒂𝒏 + 𝒃 = 𝒂 𝒏 −𝟑𝒏 + 𝟏 = 𝒂 𝒏 𝑻𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, 𝒕𝒉𝒆 𝒈𝒆𝒏𝒆𝒓𝒂𝒍 𝒕𝒆𝒓𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒆𝒒𝒖𝒆𝒏𝒄𝒆 −𝟐, −𝟓, −𝟖, −𝟏𝟏, . . . is 𝒂 𝒏 = 𝟏 − 𝟑𝐧