finance wrote:S is an infinite sequence, in which the value of a particular member of the sequence is equal to the difference between the two preceding members of the sequence. What is the value of the 43rd member of the sequence?
(1) The 1st term is 1.
(2) The 3rd term is 3.
Write out enough of the sequence to determine whether there's a repeating pattern.
Statement 1: 1st term is 1.
Let 2nd term = 2.
The sequence repeats in a pattern of 6: 1,2,1,-1,-2,-1...1,2,1,-1,-2,-1...
Since 6*7=42, the pattern repeats 7 times through term 42.
Since the 43rd term is the beginning of the pattern, the 43rd term is the same as the first term.
Thus, the 43rd term = 1.
Let 2nd term = 50.
The sequence repeats in a pattern of 6: 1,50,49,-1,-50,-49...1,50,49,-1,-50,-49...
Now we can see the nature of the pattern.
Within each pattern of 6, the last 3 terms simply change the signs of the first 3 terms.
Since the difference between the 2nd and 3rd terms is 1, the difference between the 6th and 5th terms must also be 1 -- and this difference yields the 43rd term.
Thus, the 43rd term = 1.
Sufficient.
Statement 2: The 3rd term is 3.
Let 1st term = 1 and 2nd term = 4.
The sequence repeats in a pattern of 6: 1,4,3,-1,-4,-3...1,4,3,-1,-4,-3..
Since 6*7=42, the pattern repeats 7 times through term 42.
Since the 43rd term is the beginning of the pattern, the 43rd term is the same as the first term.
Thus, the 43rd term = 1.
Let 1st term = 2 and 2nd term = 5.
The sequence repeats in a pattern of 6: 2,5,3,-2,-5, -3...2,5,3,-2,-5,-3...
Now we can see the nature of the pattern.
Within each pattern of 6, the last 3 terms simply change the signs of the first 3 terms.
Since the difference between the 2nd and 3rd terms equals the 1st term, the difference between the 6th and 5th terms must also equal the 1st term -- and this difference yields the 43rd term.
Thus, the 43rd term = the 1st term.
Since the 1st term in statement 2 can be any value, insufficient.
The correct answer is
A.
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