2008 iTest Problems/Problem 43
Problem
Alexis notices Joshua working with Dr. Lisi and decides to join in on the fun. Dr. Lisi challenges her to compute the sum of all terms in the sequence. Alexis thinks about the problem and remembers a story one of her teachers at school taught her about how a young Karl Gauss quickly computed the sum in elementary school. Using Gauss's method, Alexis correctly finds the sum of the terms in Dr. Lisi's sequence. What is this sum?
Note: Dr. Lisi’s sequence is
Solution
The first term is and the common difference is , so the term is . Using the arithmetic series formula, the sum of the terms in Dr. Lisi's sequence is .
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 42 |
Followed by: Problem 44 | |
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