MathDB
Combinatorics

Source:

December 31, 2004
arithmetic sequence

Problem Statement

By definition, r! \equal{} r(r \minus{} 1) \cdots 1 and \binom{j}{k} \equal{} \frac {j!}{k!(j \minus{} k)!}, where r,j,k r,j,k are positive integers and k<j k < j. If (n1),(n2),(n3) \binom{n}{1}, \binom{n}{2}, \binom{n}{3} form an arithmetic progression with n>3 n > 3, then n n equals <spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 7<spanclass=latexbold>(C)</span> 9<spanclass=latexbold>(D)</span> 11<spanclass=latexbold>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 5\qquad <span class='latex-bold'>(B)</span>\ 7\qquad <span class='latex-bold'>(C)</span>\ 9\qquad <span class='latex-bold'>(D)</span>\ 11\qquad <span class='latex-bold'>(E)</span>\ 12