course Mth 151
6/19 10
Question: `q001. Note that there are 6 questions in this assignment. Find the likely next element of the sequence 1, 2, 4, 7, 11, ... .
Your solution:
Each number is increased by the next counting number 1+1=2, 2+2=4, 4+3=7, 7+4=11, so next in line would be 11+5= 16
3
Ok
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Question: `q002. Find the likely next two elements of the sequence 1, 2, 4, 8, 15, 26, ... .
Your solution:
The difference of each of the numbers given is equal to the sequence of problem one so you must extend the sequence from the first problem. So you take 16+26=42 then do 16+6=22 which gives you 22+42= 64 so the next two in the sequence is 42 and 64
1
Ok
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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.
Your solution:
Each number is multiplied by 2 1x2=2 2x2=4.. so the next likely would be 8x2=16
1
Ok
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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.
Your solution:
The ratio is 1.5, 1.5, 1.5 because 108/72=1.5 and the same is for the other numbers. Then next number would be 108x1.5= 162
3
Ok
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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.
Your solution:
2/1=2 3/2=1.5 5/3=1.6 8/5= 1.6 13/8= 1.625 21/13= 1.615 is the ratio sequence
If we notice that the 3rd ratio is between the first and second ratio then we notice this is true for the other ratio so we can pick any number between 1.625 and 1.615 so we could use 1.620 and multiply that by 21 and get our next number 34.02 and round to 34 so it can be a whole number.
2
Ok
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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?
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Your solution:
You add the number to the one before it 1+0=1 1+1=2 2+1=3 3+2=5…. So 34+21= 55 55+34= 89 and 89+34= 144
3
Ok
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