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 $2008$ 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 $1+2+3+\cdots+98+99+100$ in elementary school. Using Gauss's method, Alexis correctly finds the sum of the $2008$ terms in Dr. Lisi's sequence. What is this sum?

Note: Dr. Lisi’s sequence is $-1776, -1765, -1754 \cdots$

Solution

The first term is $-1776$ and the common difference is $11$ , so the $2008^\text{th}$ term is $-1776 + 11 \cdot 2007$ . Using the arithmetic series formula, the sum of the $2008$ terms in Dr. Lisi's sequence is $\tfrac{2008(-1776-1776+11\cdot 2007)}{2} = \boxed{18599100}$ .

2008 iTest (Problems)
Preceded by: Problem 42	Followed by: Problem 44
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2008 iTest Problems/Problem 43

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