Exercises 11 12

course Mth 151

Math 151 Exercise 1.13. Inductive

5.deductive

6. Deductive

9. Inductive

10. inductive

12. Inductive

15. 21

18. 0

21. 11/12

24. 56

25. 52

27. 5

30.-4,5, -6,7, -8,9

33. (3367 X 15)=50,505

35. (33,334 X 33,334)=1,111,155,556

36. (11,111 X 11,111)=123,454,321

39. (6X1296)-1=7,775

40.

42. 5/6

45. 320,400

48. Add the remainder to the number which was divided by two in each case.

50. 5100

51. The next block should go in the lower right hand side corner block and will have seven colored blocks.

54. E,T

55.(a)The middle digit is always 9, and the sum of the first and third digits is always 9. (b) A number always divisible and also can be multiplied by 27 and 33 what is it? 891

57.142,857 x 1=142,857

b. 142,857 X 2=285,714

c. 142,857 X 3=428,571

d. 142,857 x 4= 571,428

e. 142,857 X5 =714,285

f. 142857 X 6=857,142

The above all have the same numbers in common as the first problem. When they are multiplied 1-6.

g.142,857 X 7=999,999

60. 40 X4=160+10=170 X 25=4250-365=3885+.25=3885.25+115=4000.25

Exercise 1.2

3.450

5. 4032

6. 3992

9. 57;99

10. n= 1= 1+3+1= 5

N= 2= 4+6+1= 11

N= 3= 9+9+1= 19

N= 4 16+12+1= 29

5th term = 29+12= 41

N= 5= 25+15+1= 41 Yes

12. 1,234 X 8 +4=9,876

15. 21 to the 2nd – 15 to the 2nd = 6 to the 3rd.

18. 4 to the 2nd + 4=5 to the 2nd – 5

20. 13 + 14+15+16 = 18 +19+21=58

21. 45,150

24. = 825(825+1)/2 = (825*826)/2= 340725

25. 51

27. 500

30. This appears to be an finite problem that is squared at the end, the cubed numbers in the second part are supposed to equal the first part.

33. 1st 2nd 3rd 4th 5th 6th 7th 8th

Triangular 1 3 6 10 15 21 28 36

Square 1 4 9 16 25 36 49 64

Pentagon 1 5 12 22 35 51 70 92

Hexagonal 1 6 15 28 45 66 91 120

Heptagonal 1 7 18 32 51 75 104 138

Octagonal 1 8 21 40 65 96 133 176

35. 8*T1 + 1 = 8 * 1 + 1 = 9 = 32

8*T2 + 1 = 8 * 3 + 1 = 25 = 52

8 * T3 + 1 = 8* 6 + 1= 49 = 72

8*T2 + 1 = 8 * 10 + 1 = 81 = 92

. 36. 1/3= 0.3 1

3/3= 1 0

6/3= 2 0

10/3=3 1

15/3= 5 0

21/3=7 0

28/3= 9 1

36/3= 12 0

45/3=15 0

.. 39. 16= 6+10

25= 10+15

36= 15+21

40. these are the square numbers from 2 to 8

2*2=4

3*3=9

4*4=16

5*5=25

6*6=36

7*7=49

8*8=64

Fractions = 4/9, 9/16,

16/25, 25/36, 36/49, 49/64

b) triangular numbers

1,3,6,10,15,21,28,36,45

Fractions = ½, ¾, 6/7,10/11, 15/16, 21/22, 28/29,36/37, 45/46

Yes all the numbers are in lowest terms

• . 42. [x) = least integer greater than or equal to the number x

 [x) = least integer not less than or equal to the number x

For−3

For−2

45. 45:= ninth pentagonal number

N(3n-1)/2= 9(3*9-1)/2= 117

48. 48:= twelfth octogonal number = n(6n-4)/2= 12(6*12-4)/2= 408

50. 81

51. if u add two triangular number what figurate the number

So we will get a number which is a square .

Two consecutive triangular numbers are 1 and 3 add 1+3= 4 is a square

3+6= 9 is a square

6+10= 16 is also square

54. take a number equal or more than 2 then multiply by 3 and add n

N= 2 number will be 2*3+2=8 =

N=3 number will be 3*3+3 = 12

N= 4 number will be 4*3+4= 16

N= 5 number will be 5*3+5= 20

The difference is same as 4

As noted elsewhere, you should be using the q_a_ and query programs to submit and explain your work. However from what I can tell in this document, you seem to be doing very well. Be sure to see my e-mail regarding your test.

Keep up the good work.