#$&*
course mth151
006. Sequences and Patterns*********************************************
Question: `q001. Note that there are 6 questions in this assignment.
Find the likely next element of the sequence 1, 2, 4, 7, 11, ... .
SOLUTION: 16. derived by addin +1,+2,+3,+4,+5,+5 etc to the previous number.
confidence rating #$&*: very confident
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Question: `q002. Find the likely next two elements of the sequence 1, 2, 4, 8, 15, 26, ... .
SOLUTION: Given numbers are 1,2,4,8,15,26. The sequence used to derive these elements is to add: 1, 2, 4, 7, 11 to the given numbers. THere is a difference of 1,2,3,4 & 5 between these numbers. We can then derive that there will be a diffence of 5,7,8,9 & 10 between the next numbers.
So, the last sequence # was 11 and we need to add 5 to 11 for 16. Then we need to add 16 to 26 for 42. 42 is the next element.
Then we need to add 6 to 16 for 22. Then we should add 22 to 42 for 64. 64 is the next element.
Then we need to add 7 to 22 for 29. Then we sholud add 29 to 64 for 93. 93 is the next element
THen we should add 8 to 29 for 37. Then we add 37 to 93 for 130. 130 is the next element.
Then we need to add 9 to 37 for 46. Then we should add 46 to 130 for 176. 176 is the next element
So, 42,64,93,130 and 176 are the next elements.
confidence rating #$&*: very confident
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Question: `q003. What would be the likely next element in the sequence 1, 2, 4, 8, ... . It is understood that while this sequence starts off the same as that in the preceding exercise, it is not the same. The next element is not 15, and the pattern of the sequence is different than the pattern of the preceding.
SOLUTION: this sequence is derived by multiplying the preceding number by 2. so the next element would be 16
confidence rating #$&*: very confident
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Question: `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.
SOLUTION: 48-32 = 16 or 32/2
72-48 = 24 or 48/2
108-72= 36 0r 72/2
?-108 = 54 or 108/2
answer = 162
confidence rating #$&*: very confident
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Question: `q005. Find the sequence of ratios for the sequence 1, 2, 3, 5, 8, 13, 21... , and estimate the next element of the sequence.
SOLUTION:
1, 2, 3, 5, 8, 13, 21 34
2+1=3 3+2=5 5+3=8 8+5=13 13+8=21 21+13 = 34
ratios: 13/8=1.625 21/13 = 1.615 ?????
the next element = 34 ; i'm not sure about the ratio part
confidence rating #$&*: very confident
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Question: `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?
SOLUTION:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
1+1 2+1 3+2 5+3 8+5 13+8 21+13 34+21 55+34 89+55
next elements are 55,89,144
confidence rating #$&*: very confident
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@& As I've explained previously, to get full feedback you need to include the entire document.
However you appear to be in good shape here.*@