## mmend98 one year ago The development studio behind the newest video game, Super Ostrich Racers, needs your help. Super Ostrich Racers is an exciting, fast-paced adventure game where your ostrich runs through 20 different levels while collecting coins. They need you to develop the number of coins and points for each level and provide data for the programming team. Create the data to fill in the tables below. The Coins table must be an arithmetic sequence and the Points table must be a geometric sequence. The common difference or ratio cannot equal 1 or 0. Provide reasons and justification of how you know the Co

1. mmend98

@ganeshie8

2. mmend98

Create the data to fill in the tables below. The Coins table must be an arithmetic sequence and the Points table must be a geometric sequence. The common difference or ratio cannot equal 1 or 0. Provide reasons and justification of how you know the Coins sequence you created is arithmetic and how you know the Points sequence is geometric. Level Coins 1 2 3 Level Points 1 2 3 Planning is crucial in the early stages of this project. Demonstrate how a recursive process will allow you to find the number of coins and points on all levels up to level 5. The development team has asked you to jump ahead of them in the project. Create the sequence formulas, an, for the coins and the points based on the level in the game. Then describe how the formula can be used to find the coins and values on level 15. Use complete sentences. If the game only has 20 levels, explain how to find the value of the series for the coins and the points. Use complete sentences and arrive at final values. The programming team needs to understand the parameters for the game, in order to start coding it. Explain any restrictions to the domain and range of your sequences

3. mmend98

this is what I have so far I need help on question 4 and question 5

4. ganeshie8

lets fix the mistakes in parts 1-3 first

5. mmend98

ok

6. ganeshie8

In part 1, below highlighted word should be "difference" right ? because "ratio" for an arithmetic sequence makes no sense |dw:1439525121495:dw|

7. mmend98

k fixed it

8. mmend98

what is next

9. ganeshie8

good, lets see part 2

10. mmend98

k

11. mmend98

Is part 2 all correct?

12. ganeshie8

nope, it is totally wrong

13. mmend98

dang haha

14. ganeshie8

you're correct about the recursive formulas but the numbers are wrong

15. mmend98

okay

16. ganeshie8

|dw:1439525341712:dw|

17. ganeshie8

where does that $$9$$ come from ?

18. mmend98

let me see

19. mmend98

I honestly don't know haha

20. ganeshie8

|dw:1439525998794:dw|

21. mmend98

its so hard to write these formulas on pages so is there anyway i could change my arithmetic series column to match this

22. mmend98

I changed them to 3,6,9

23. mmend98

and 2 4 8

24. ganeshie8

Ahh okay, please attach the updated pdf so that it will be less confusing

25. mmend98

kk

26. mmend98

27. mmend98

@ganeshie8

28. ganeshie8

parts 1,2,3 look okay now but your teacher can easily guess that you have copy pasted that stuff from internet

29. ganeshie8

|dw:1439526431634:dw|

30. ganeshie8

you seriously need to rephrase that into ur own words

31. mmend98

ok

32. mmend98

just completed that

33. ganeshie8

okay good, whats the part 4 ?

34. mmend98

i havent completed it yet. let me attach the question

35. ganeshie8

can you copy paste only the part 4 question here

36. mmend98

If the game only has 20 levels, explain how to find the value of the series for the coins and the points. Use complete sentences and arrive at final values.

37. ganeshie8

remember, the word series refers to sum

38. mmend98

ok

39. ganeshie8

so basically you need to find the sum of first 20 terms

40. ganeshie8

look up your notes for "sum" formulas of arithmetic series and geometric series

41. mmend98

do i use this formula ?

42. ganeshie8

yes, what formula ?

43. mmend98

44. ganeshie8

there is another formula, look it up

45. mmend98

this one

46. mmend98

47. ganeshie8

nope

48. mmend98

haha which one do i use. do i use the same formula for question 3?

49. ganeshie8

for arithmetic series, it should look something like below : $S_n = \dfrac{n}{2}[2a+(n-1)d]$

50. mmend98

ahh how do i put my numbers into this

51. mmend98

if u don't mind putting them in i will calculate

52. ganeshie8

do you know that exactly are we finding here ?

53. mmend98

what?

54. mmend98

we are trying to find the value of the series for the coins and the point

55. ganeshie8

we want to find below sum : $3+6+9+\cdots (\text{upto 20 terms})$

56. ganeshie8

whats the first term ?

57. mmend98

correct

58. mmend98

the first term is 3

59. ganeshie8

so $$a=3$$

60. ganeshie8

whats the common difference ?

61. mmend98

3

62. ganeshie8

so $$d=3$$

63. ganeshie8

how many terms are there in the sum ?

64. mmend98

20

65. ganeshie8

so $$n=20$$ plug them in the formula, the formula gives you the sum

66. mmend98

ok let me calculate real quick

67. ganeshie8

$S_n = \dfrac{n}{2}[2a+(n-1)d]$ $S_{20} = \dfrac{20}{2}[2*3+(20-1)*3]$

68. mmend98

s20=7.5?

69. mmend98

sorry one sec

70. mmend98

haha 750

71. mmend98

s20=750?

72. ganeshie8

try again

73. mmend98

3420

74. mmend98

geez

75. mmend98

i think thats correct @ganeshie8

76. mmend98

how do i change that formula for geometric series @ganeshie8

77. ganeshie8

time to burn ur calculator

78. ganeshie8

$S_n = \dfrac{n}{2}[2a+(n-1)d]$ $S_{20} = \dfrac{20}{2}[2*3+(20-1)*3]$ wolfram says that evaluates to 630 http://www.wolframalpha.com/input/?i=+%5Cdfrac%7B20%7D%7B2%7D%5B2*3%2B%2820-1%29*3%5D

79. mmend98

okay now what is the formula for geometric

80. ganeshie8

look up in your notes for "partial sum of geometric series formula"

81. mmend98

this it?

82. mmend98

i am sorry for my slowness i just really am trying to get this done

83. ganeshie8

nope, use this : $S_n = a_1\dfrac{r^n-1}{r-1}$ where $$a_1$$ = first term $$r$$ = common ratio $$n$$ = number of terms

84. mmend98

okay so how would i plug this in

85. mmend98

what would m common ratio be

86. ganeshie8

|dw:1439528427488:dw|

87. mmend98

k

88. ganeshie8

plug them in and evaluate

89. mmend98

okay.

90. mmend98

Sn=2 (2^20-1)/(2-1)?

91. mmend98

i don't think i plugged it in right lol

92. mmend98

93. ganeshie8

what do you get ?

94. ganeshie8

outrageous number for the sum is expected because this is a geometric series grows super fast

95. mmend98

2,097,150

96. ganeshie8

Perfect!

97. mmend98

yes okay great.

98. mmend98

I have question 5 now then i am done

99. mmend98

The programming team needs to understand the parameters for the game, in order to start coding it. Explain any restrictions to the domain and range of your sequences.

100. ganeshie8

for restrictions on domain, look at first column |dw:1439528857139:dw|

101. ganeshie8

what numbers are allowed in that column ?

102. ganeshie8

can you have 1.5 ?

103. mmend98

no

104. ganeshie8

or -2 ?

105. mmend98

no

106. mmend98

so how would i express that as my answer

107. ganeshie8

domain is all the "inputs" that are allowed for the function to eat so whats the domain in our problem ?

108. mmend98

the domain is 1,23,..?

109. mmend98

There would be no restriction on the range. The domain for the points would be andy integer that is greater than or equal to 1, like 1,2,3,4,5,..etc.

110. mmend98

would this work for my answer ? @ganeshie8

111. ganeshie8

Looks good! the domain is all positive integers : 1, 2, 3, 4, 5,...

112. ganeshie8

|dw:1439529213392:dw|

113. mmend98

okay we are finished ! There would be no restriction on the range. The domain for the points would be any positive integer that is greater than or equal to 1, like 1,2,3,4,5,..etc.

114. mmend98

Right?

115. ganeshie8

there are rstrictions on range too

116. mmend98

dang it

117. mmend98

what are they haha

118. ganeshie8

restrctions for range of arithmetic sequence : |dw:1439529300043:dw|

119. mmend98

what does that mean

120. ganeshie8

range is also positive integers, for arithmetic sequences the range is only the multiples of 3 for geometric sequence the range is only the powers of 2

121. ganeshie8

please attach the updated the pdf if you want me check

122. mmend98

k

123. mmend98

124. mmend98

here it is @ganeshie8

125. ganeshie8

Looks okay!

126. mmend98

thanks i really appreciate you.. life saver

127. ganeshie8

yw