7. The progression is 6, 63, 7, 8, 83, 91, 10. 8. The progression is 5, 7, 9, 11, &c., all the odd numbers 14. 8 days. 15. 5 days and 10 days; 55 miles and 80 miles. qn. 1 Let the learner verify the preceding formulæ, by making a=2, q=3, n = = 3, 7 = 18, and S=26. SECTION LIII. ART. 152. 1. 7=640; S=1275. 2. 1=;8=1ff. 3. 2, 10 and 50. 4. $4095. 5. Performed. 6. 3, 15, 75, 375 and 1875. 7. 7, 35 and 175. 8. 8, 24 and 72. 9. Any progression in which the ratio is 2. 10. 3, 5 and 7. 11. 6. 12. 10. 13. 7.937+. 14. 178-535+. 15. 2. 16. 6. 17. 21. 18.914. 19. Progression 2, 6, 18, 54, 162. 20. Progression 5, 30, 180, 1080. 21. Progression 3, 15, 75, 375, 1875, 9375, 46875. 22. Progression 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. SECTION LIV. ART. 153. 3 1st to 5th inclusive, performed. 18. 3, or 19. 6. 626. 12th to 15th inclusive, performed. 23. 2, or -3. 16. 2, or -3. 17. ±√2, or +/-6. 24. 25, or 81. 3. x 18, y=3; or x = 12, y = — 21. =2, y = 3; or x —— 46, y = 15. 4. x= 5. x = 4, y= = 2; or x=— -4, y = — 2. 6th to 11th inclusive, performed. 12. x 6, y=3; or x=-6, y=-3. = 13. x=7, y=3; or x=3, y=7. ·3, 14. x 3, y=5; x=-3, y=-5; x=5, y=3; or x=-5, y=—3. 15. x=9, y=3; or x=— 9, y=-3. 16. x 49, y = = 25.. 17. x= 625, y = 16. - 4. 18. x=5, y=4; or x=— -5, y= == 19. x=7, y=3; or x=-3, y=—7. 20. x1,y=2; x = −1, y = 2; x = 2, y = 1; or x=2, y = 1. 21. x=2, y=4; x=4, y=2; x=3+\/21,y=3−√/21; or x=3—√/21, y=3+√/21. 22. x=1, y = 2; or x = 2, y = 1. 23. x 4, y=9; or x=9, y = 4. = 24. x= 8, y = 2; or x = 2, y = 8. 25th and 26th performed. 27. x 20, y = 16. = 28. x5, y3. 29. x=8, y=6; x = −8, y = −6 ; x = 6, y=8; or X=- - 6, y = - 8. 30. x 14, y = 12. = 31. x=27, y = 148; or x=6, y = 33. 32. x5, y = ±3. 33. Performed. 34. x=3, y=1; x=−3, y=−1; x=8√t, y=√ễ; or x=-8√ễ, y = — √ễ. 35. x4, y=3; x=-4, y=-3; x, y = 3; or x=4,y=-3. 11 36. x1,y=2; x=-1,y=-2; x = 3, y=4; or x, y = y. - ''. 37. x=4, y=2; x=—4, y=—2; x=−√7,y=√7; or x = √7, y=—√7. |