Question 475946: for each given set,how do I choose the set with the same cardinality
{1,4,7,...,91,94} Possible choices
{1,2,3,...,205,206} {131,132,133,...,247}
{1,3,5,...,211,213} {147,148,149,...,240}
{3,4,5,...34}
{131,132,133,...,237}
{1423,1425,1427,...,1833}
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! By the given patterns, you should be able to determine the size of each set.
For example: the size of {1,2,3,...,205,206} is obviously 206.
So you need to figure out the sizes of all sets including {1,4,7,...,91,94}, {1423, 1425, 1427,...,1833} and {1,3,5,...,211,213} which are the hardest ones.
To do them, here's a hint, consider the formula for the general term of an arithmetic sequence: a(n) = a(1) + (n-1)*d, which basically says that the nth term of the sequence is the first term plus the difference times the amount of terms that already exist, namely (n-1), and of course the difference is the difference between the successive terms.
For {1,4,7,...,91,94} we have the first term equal to 1, and the last term is 94, the common difference between each successive term is 3, so now we can work backwards to figure out which numbered term 94 is. Once we do this, we essentially have the size of the set. We know the formula given above must hold, therefore 94=1+(n-1)*3...(I'll let you do the algebra here and just give the answer, but you should check and make sure you come to the same conclusion in order to determine the sizes of the other sets)...we get n = 32. So therefore, we have the size of this set as 32.
So now you have to find another set with size 32 and that's the set your looking for.
Good Luck!
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