2008 iTest Problems/Problem 42
Problem
Joshua's physics teacher, Dr. Lisi, lives next door to the Kubiks and is a long time friend of the family. An unusual fellow, Dr. Lisi spends as much time surfing and raising chickens as he does trying to map out a . Dr. Lisi often poses problems to the Kubik children to challenge them to think a little deeper about math and science. One day while discussing sequences with Joshua, Dr. Lisi writes out the first terms of an arithmetic progression that begins . Joshua then computes the (positive) difference between the term in the sequence, and the term in the sequence. What number does Joshua compute?
Solutions
Solution 1
To get from the term to the term, add . To get from the term to the term, add . To get from the term to the term, add . Thus, the (positive) difference between the term in the sequence and the term in the sequence is .
Solution 2
The explicit formula of the arithmetic series is Using this formula, the is and the term is . The difference between the two terms is .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 41 |
Followed by: Problem 43 | |
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