Which of the following methods can be used to construct a pattern of 10 numbers for which it would be mathematically impossible to predict the 11th term?
(more then one answer.)
A.Make a pattern, starting with 3, where each number is the next digit of pi (3.14159 . . .).
B.Make a pattern by asking each of 10 friends what their favorite number is.
C.Make a pattern by counting the number of letters in each word of Lincoln's Gettysburg Address, starting with the first word.
D.Make a pattern based upon values assigned to the current weather.
E.Make a pattern where each number is the square of the number before it, plus 7 times the cube of the number before that.
I'd say B and D, subject to a few assumptions
4. What is the value of the 11th term in the sequence?
-1 , 5 , 11 , 17 , 23 , ...
C. Make a pattern by counting the number of letters in each word of Lincoln's Gettysburg Address, starting with the first word.
D. Make a pattern based upon values assigned to the current weather.
To determine which methods can be used to construct a pattern of 10 numbers for which it would be mathematically impossible to predict the 11th term, we need to understand the characteristics of each method.
A. Making a pattern using the digits of pi (3.14159...) will result in a sequence that is mathematically determined and predictable. Each subsequent digit in pi is already known and follows a specific sequence, so it is possible to predict the 11th term.
B. Making a pattern based on asking friends for their favorite numbers is subjective and unpredictable. Each friend might choose a different number, making it impossible to predict the 11th term without additional information. This method can result in an unpredictable sequence.
C. Making a pattern based on the number of letters in each word of Lincoln's Gettysburg Address can lead to an unpredictable sequence. However, since the words and their letter count are predetermined, it is theoretically possible to analyze the sequence and predict the 11th term. So, this method may not guarantee the impossibility of predicting the 11th term.
D. Making a pattern based on current weather values may seem unpredictable, but weather patterns can be analyzed and predictions can be made based on historical data and scientific models. Therefore, it is not impossible to predict the 11th term using this method.
E. Making a pattern where each number is derived from the square of the previous number, plus 7 times the cube of the number before that can result in complex calculations and sequences. Without a clear formula or pattern, it may be difficult or impossible to predict the 11th term analytically. This method offers the possibility of an unpredictable sequence.
From the given options, the methods that can potentially lead to a pattern for which it would be mathematically impossible to predict the 11th term are:
- B. Make a pattern by asking each of 10 friends what their favorite number is.
- E. Make a pattern where each number is the square of the number before it, plus 7 times the cube of the number before that.