1997 AHSME Problems/Problem 6: Difference between revisions

Latest revision as of 13:12, 5 July 2013

Consider the sequence

$1,-2,3,-4,5,-6,\ldots,$

whose $n$ th term is $(-1)^{n+1}\cdot n$ . What is the average of the first $200$ terms of the sequence?

$\textbf{(A)}-\!1\qquad\textbf{(B)}-\!0.5\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ 0.5\qquad\textbf{(E)}\ 1$

The average of a list is the sum of all numbers divided by the size of the list.

The sum of the list can be found by adding the numbers in pairs: $(1 + -2) + (3 + -4) + ... + (199 + -200)$

The sum of each pair is $-1$ , and there are $100$ pairs, so the total sum is $-100$ .

There are $200$ numbers on the list, so the average is $\frac{-100}{200} = -0.5$ , and the answer is $\boxed{B}$

1997 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AHSME Problems and Solutions

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 == See also ==
 {{AHSME box|year=1997|num-b=5|num-a=7}}
+{{MAA Notice}}