course Mth 151 ûàûìÖÙäLëðÄc¼‘®ë™‰Üªk‰Íâåassignment #006
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16:02:45 `q001. Note that there are 6 questions in this assignment. Find the likely next element of the sequence 1, 2, 4, 7, 11, ... .
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RESPONSE --> Next likely element would be 16. The numbers are increasing by adding, 1 then 2 then 3 to the preceding number. confidence assessment: 3
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16:03:01 The difference between 1 and 2 is 1; between 2 and 4 is 2; between 4 and 7 is 3; between 7 and 11 is 4. So we expect that the next difference will be 5, which will make the next element 11 + 5 = 16.
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RESPONSE --> self critique assessment:
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16:10:15 `q002. Find the likely next two elements of the sequence 1, 2, 4, 8, 15, 26, ... .
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RESPONSE --> The next like two elements would be 32 & 64. T confidence assessment: 3
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16:12:46 `q003. What would be the likely next element in the sequence 1, 2, 4, 8, ... . It is understood that while this sequence starts off the same as that in the preceding exercise, it is not the same. The next element is not 15, and the pattern of the sequence is different than the pattern of the preceding.
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RESPONSE --> The next likely element would be 16 because the sequence appears to be mutiples of 2. confidence assessment: 3
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16:34:19 `q004. There are two important types of patterns for sequences, one being the pattern defined by the differences between the numbers of the sequence, the other being the pattern defined by the ratios of the numbers of the sequence. In the preceding sequence 1, 2, 4, 8, 16, ..., the ratios were 2/1 = 2; 4/2 = 2; 8/4 = 2; 16/8 = 2. The sequence of ratios for 1, 2, 4, 8, 16, ..., is thus 2, 2, 2, 2, a constant sequence. Find the sequence of ratios for the sequence 32, 48, 72, 108, ... , and use your result to estimate the next number and sequence.
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RESPONSE --> The sequence is 16, 24, 36. The ratios would be 32/16 = 2, 48/24 = 2, 72/36 =2, 108/54 = 2. The next element would be 160. confidence assessment: 2
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16:37:23 `q005. Find the sequence of ratios for the sequence 1, 2, 3, 5, 8, 13, 21... , and estimate the next element of the sequence.
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RESPONSE --> The raito would be 1+2=3, 2+3=5, 3+5=8, 5+8=13, 13+8=21. The next element would be 13+21=34. confidence assessment: 3
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16:39:27 `q006. Without using ratios, can you find a pattern to the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ..., and continue the sequence for three more numbers?
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RESPONSE --> The three next numbers would be 55, 89, 144. You are adding the two preceeding #s. confidence assessment: 3
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