Expert: Sherman D. - 6/11/2009

Question
12. Determine the sum for the arithmetic series:
n = 30, t1 = 25, t30 = 228


13. Determine the sum for the arithmetic series:
n = 44, t1 = 13, t44 = 400


14. Determine the sum for the arithmetic series:
n = 37, t1 = 23, t37 = 203


15. Express as an equation: The parabola with focus (0,-1) and directrix y = 1  

16. Determine the sum for the arithmetic series:
n = 100, t1 = 17, t100 = 215

17. Determine the sum for the arithmetic series:
n = 50, t1 = 187, t50 = 40


19. Determine the sum for the geometric series:
n=10, r=-2, t1=1

20. Determine the sum for the geometric series:
n=12, r=3, t1=1/10

22. Find S20 if the series 1+1.1+... is arithmetic.

23. Find the sum for the positive two-digit integers ending in 4.

24. Find the sum for the positive three-digit integers divisible by 6.

25. Determine the sum for the positive two-digit integers that are not divisible by 5.

26. Kirsten is given a test consisting of 15 questions. The first question is worth 5 points, and each question after the first is worth three points more than the question before it. What is the maximum score that Kirsten can obtain?

27. A ship's clock strikes every half hour of a 4-hour period. After the first half hour it strikes "one bell," after another half hour it strikes "two bells," and so on until it strikes "eight bells" at the end of the four hour period. It then begins a new four hour period . How many strikes of the bell occur in one day?

28. Determine the sum for the geometric series: 27+18+12+8+...  


29. Determine the sum for the geometric series: 1/2 - 1/3 + 2/9 - 4/27 + ...  


30. Find the first three terms of the infinite geometric series satisfying the condition: r = 2/5, s = 125  

33. Write the series in sigma notation:
The series consisting of positive three-digit integers divisible by 5.


34. Find the sum of the series. If there is no sum, say so.
3++5 1/3+7 1/9+...  

Answer
12. Determine the sum for the arithmetic series:
n = 30, t1 = 25, t30 = 228

S(30) = (30/2)(25 + 228)
S(30) = 3795

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13. Determine the sum for the arithmetic series:
n = 44, t1 = 13, t44 = 400

S(44) = (44/2)(13 + 400)
S(44) = 9086

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14. Determine the sum for the arithmetic series:
n = 37, t1 = 23, t37 = 203

S(37) = (37/2)(23 + 203)
S(37) = 4181

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15. Express as an equation: The parabola with focus (0,-1) and directrix y = 1  

y = (-1/4)x^2

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16. Determine the sum for the arithmetic series:
n = 100, t1 = 17, t100 = 215

S(100) = (100/2)(17 + 215)
S(100) = 11600

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17. Determine the sum for the arithmetic series:
n = 50, t1 = 187, t50 = 40

S(50) = (50/2)(187 + 40)
S(50) = 5675

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19. Determine the sum for the geometric series:
n=10, r=-2, t1=1

S(10) = (1 - (-2)^10)/(1 - (-2))
S(10) = -341

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20. Determine the sum for the geometric series:
n=12, r=3, t1=1/10

S(10) = ((1/10) * (1 - 3^(12)))/(1 - 3)
S(10) = 26572

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22. Find S20 if the series 1+1.1+... is arithmetic.

a(20) = 1 + .1(20 - 1)
a(20) = 2.9

S(20) = (20/2)(1 + 2.9)
S(20) = 3

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23. Find the sum for the positive two-digit integers ending in 4.

i'm assuming you mean 14, 24, 34, 44, 54, ... 94

a(n) = 14 + 10(n - 1)

94 = 14 + 10(n - 1)
80 = 10(n - 1)
8 = n - 1
n = 9

S(9) = (9/2)(14 + 94)
S(9) = 486

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24. Find the sum for the positive three-digit integers divisible by 6.

i'm assuming you mean

102, 108, 114, 120, ... 996

a(n) = 102 + 6(n - 1)
996 = 102 + 6(n - 1)
894 = 6(n - 1)
149 = n - 1
n = 150

S(150) = (150/2)(102 + 996)
S(150) = 82350

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25. Determine the sum for the positive two-digit integers that are not divisible by 5.

11, 12, 13, 14, 16, 17, 18, 19, 21 ... 99

lets do this

S(90) = (90/2)(11 + 99)
S(90) = 4950

but were not done yet

10, 15, 20, 25, 30, 35, ... 95

S(9) = (9/2)(10 + 90) + (9/2)(15 + 95)
S(9) = (18/2)(100 + 110)
S(9) = 1890

now we just subtract 1890 from 4950

ANS : 3060

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26. Kirsten is given a test consisting of 15 questions. The first question is worth 5 points, and each question after the first is worth three points more than the question before it. What is the maximum score that Kirsten can obtain?

a(15) = 5 + 3(15 - 1) = 47

S(15) = (15/2)(5 + 47)
S(15) = 390

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27. A ship's clock strikes every half hour of a 4-hour period. After the first half hour it strikes "one bell," after another half hour it strikes "two bells," and so on until it strikes "eight bells" at the end of the four hour period. It then begins a new four hour period . How many strikes of the bell occur in one day?

1, 2, 3, 4, .... 48, by the end of the day, there will be 48 rings

S(48) = (48/2)(1 + 48)
S(48) = 1176

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28. Determine the sum for the geometric series: 27+18+12+8+...  

a(n) = 27 * r^(n - 1)
a(2) = 27 * r
18 = 27r
r = (2/3)

a(3) = 27 * (2/3)^2
12 = 12

S(∞) = 27/(1 - (2/3)) = 81

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29. Determine the sum for the geometric series: 1/2 - 1/3 + 2/9 - 4/27 + ...  

a(2) = (1/2)r
(-1/3) = (1/2)r
r = (-2/3)

a(3) = (1/2)(-2/3)^2
(2/9) = (1/2)(4/9)

a(4) = (1/2)(-2/3)^3
(-4/27) = (1/2)(8/27)
(-4/27) = (-4/27)

S(∞) = (1/2)/(1 - (-2/3))
S(∞) = (3/10)

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30. Find the first three terms of the infinite geometric series satisfying the condition: r = 2/5, s = 125  

125 = a1/(1 - (2/5))
a1 = 75

a(2) = 75 * (2/5)
a(2) = 30

a(3) = 75 * (2/5)^2
a(3) = 12

ANS : 75, 30, 12

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33. Write the series in sigma notation:
The series consisting of positive three-digit integers divisible by 5.

100, 105, 110, ... 995

a(n) = 100 + 5(n - 1)
995 = 100 + 5(n - 1)
895 = 5(n - 1)

there are 178 possible values

178
 Σ (5n + 95)
n - 1

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34. Find the sum of the series. If there is no sum, say so.
3 + 5 1/3 + 7 1/9 + ...
3 + (16/3) + (64/9)

i'm not certain about the pattern of the series. So i'd so no sum. check with answers.yahoo.com to see what they say. along with the rest of the answers i have given just to be sure.