course Mth 151
6/19 11
Question: `qQuery 1.2.6 seq 2, 57, 220, 575, 1230, 2317 ... by successive differences Your solution:
2, 57, 220, 575, 1230, 2317, # 3992
55, 163, 355, 655, 1087, # 1675
108, 192, 300, 432, # 588
84, 108, 132, # 156
24, 24,
You do 57-2 to get the numbers for line 2 so the next term is 3992
3
Tell what each line equals
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Question: `q1.2.18 1^2 + 1 = 2^2 - 2; 2^2 + 2 = 3^2 - 3; 3^2 + 3 = etc.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
4^2 + 4 would come next then 5^ 2 – 5
2
Show the chart
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Question: `q1.2.30 state in words (1 + 2 + ... + n ) ^ 2 = 1^3 + 2^3 + ... + n^3
Your solution:
square of the sum of the first n counting numbers is equal to the sum of their cubes
3
Ok
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Question: `q1.2.36 1 st triangular # div by 3, remainder; then 2d etc. Pattern.
Your solution:
Triangle numbers are 1, 3, 6, 10 if you divide 1 by 3 you get 0 are the remainder is one if you divide 3 by 3 you get 1 with the remainder with remainder of 0 if you divide 6 by 3 you get 2 with the remainder of 0 then 10 divided by 3 with remainder of 1 the pattern is 1, 0, 0, 1,
3
Ok
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Question: `q1.2.48 use formula to find the 12 th octagonal number. Explain in detail how you used the formula to find this number.
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Your solution:
The formula is Octagonal #'s: n / 2 * [ 6n - 4 ]
You plug in 12 for n so its 12/2*[6(12)-4] which give you 6*[72-4] 6*68= 408
3
Ok
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