2007 AMC 12A Problems/Problem 7

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Problem

Let $a, b, c, d$ , and $e$ be five consecutive terms in an arithmetic sequence, and suppose that $a+b+c+d+e=30$ . Which of $a, b, c, d,$ or $e$ can be found?

$\textrm{(A)} \ a\qquad \textrm{(B)}\ b\qquad \textrm{(C)}\ c\qquad \textrm{(D)}\ d\qquad \textrm{(E)}\ e$

Solution

Let $f$ be the common difference between the terms.

$a=c-2f$
$b=c-f$
$c=c$
$d=c+f$
$e=c+2f$

$a+b+c+d+e=5c=30$ , so $c=6$ . But we can't find any more variables, because we don't know what $f$ is. So the answer is $\textrm{C}$ .

2007 AMC 12A (Problems)
Preceded by Problem 6	Followed by Problem 8
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2007 AMC 12A Problems/Problem 7

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