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7. The progression is 6, 65, 71, 8, 83, 94, 10.

8. The progression is 5, 7, 9, 11, &c., all the odd numbes to 41 inclusive.

9. 300 strokes. 10. 950 trees. 11. 31700 feet. 12. 16081 13. S= an?. 14. 8 days. 15. 5 days and 10 days; 55 miles and 80 miles. 16. 12, 17, 22. 17. 4, 6 and 8. 18. 14, 12, 10, 8 and 6. 19. 531.

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T VI" -va" 2. 9= =V i

S=

V-va 7

1(q” — 1) 3. á =

S

qu(9-1) S(9–1) Sq4. az

q"

.; Let the learner verify the preceding formulæ, by making a=2, q=3, n = 3,1=18, and S=26.

9" —1

9" - 1

SECTION LIII.

Art. 152.

1. 1=640; S= 1275. 2.1=;S=141.

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. 911. 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.
1st to 5th inclusive, performed. 18. 3, or ♡ — 19.
6. 626.

19 25, or 49.
7. 10, or 2.
8. 4.

20. +8, or EV – 1331. 9.

21. 729, or (-4)6. 10. 9.

22. 3, or o—41. 11. 81. 12th to 15th inclusive, performed. 23. 2, or — 3. 16. 2, or 3.

24. 25, or 81. 17. EV2, or EV – 6. 25. (& EV - 47)3

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2 a

26. 27, or (78)*
27. (+Y724)
28. 81, or (-6)*.
29. 4, or 4.
30. 4, or 1.
31.

(

EV62 +4ac_6 . 32d and 33d performed. 34. 9, or

- 12. 35. 10, or

-2. 36. 1, or 1+V60. 37. 6, or

- 9. 38. 9, or 5 + 25.

+377 - 1 39. 5, or -6, or

2

5 +1329 40. 3, or -3, or

4

SECTION LV.

Art. 154.

1. Performed. 2. x= 21, y=4; or x = 2, y = 5. 3. x = 18, y = 3; or x = 121, y=-21. 4. x=2, y = 3; or x = -46, y = 15. 5. 2= 4, y = 2; or x=-4, y=-2. 6th to Ilth inclusive, performed. 12. x=6, y= 3; or r=-6, y=-3. 13. x=7, y= 3; or x= 3, y=7. 14. =3, y=5; x = -3, y=-5; 1= 5, y = 3; or r=-5, y=-3.

15. x=9, y=3; or x=-9, y=-3.
16. x == 49, y = 25..
17. x= 625, y = 16.
18. r=5, y=4; or r=-5, y=- 4.
19. 1=7, y=3; or x=-3, y=-7.

20. 1=1, y=2; x=-1, y=-2; x=2, y=1; or =-2, y = -1.

21. r=2, y=4;2=4, y=2; 2=3+V21, y=3-V21; or c=3-V21, y=3+V21.

22. x= 1, y = 2; or x = 2, y=1.
23. <= 4, y = 9; or x=9, y=4.
24. x=8, y = 2; or <= 2, y=8.
25th and 26th performed.
27. x =

20, y = 16. 28.

5, y = 3. 29. 1=8, y=6; 1= -8, y=-6; 1=6, y=8; or - 6,

y=- -8. 30. X =

: 14, y = 12. 31. 1= 27, y = 1484; or 1=6, y= 33. 32. x = 5, y=+3. 33. Performed.

34. x= 3, y=1; 1=-3, y=-1; 1=8Vē, y=Vā; or r=-8Vł, y=-VĪ.

35. x= 4, y = 3; 1=-4, y=-3; 1= 4, y = 3; or I=-1, y=-3.

36. 1=1, y=2; 1= -1, y= -2; 1= }, y=-1; or x=-3, y=.

37. r=4, y=2; 1=—4, y=-2; 1=-17, y=v7; or x=V7, y=-17.

SECTION LVI.

AR'r. 155.

1. 2048. 2. 65536. 3. 1048576. 4. 4194304. 5. 131072. 6. 4194304. 7. 32. 8. 32. 9. 16. 10. 1024. 11. 16. 12. 64.

13. 32768.
14. 16384.
15. 65536.
16. 1048576.
17. 1048576.
18. 1048576.
19. 32.
20. 8.
21. 8.
22. 16.
23. 8.
24. 8.

SECTION LVII.

Art. 162.
1. 3.1048284.

6. 4.1041671. 2. 4.7581015.

7. 0:4392806. 3. 2:1048284.

8. 2:5228783. 4. 3.4456042.

9. 2.6389892. 5. 55152060.

10. 2:0467815 Art. 163. 1. 30.

6. 1.03472. 2. 2000.

7. 03048. 3. 31:55888.

8. 0.0593562. 4. 1309.534.

9. 0.0016891. 5. 221754.6.

10. 0.0002155. ART. 167.

1. 1.8593785, or 9.8593785. 3. 1.5789370, or 6:5789370 2. 3.7604225, or 7.7604225. 4. 1.8239087, or 9.8239087

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