# ( left{x mid x=frac{3 p+1}{2 p-1}, p in W text { and } p leq 5right} ; ) Roster form

( begin{aligned} text { } quad text { Let } & A=left{x mid x=frac{3 p+1}{2 p-1}, quad p in omega, quad p leq 5right} & therefore quad p in omega, quad p leqslant s-end{aligned} )

( p=0,1,2,3,4,5 )

Fer ( p=0, quad x=frac{3(0)+1}{2(0)-1}=frac{1}{-1}=-1, quad(-1,0) in A )

( P=1, quad x=frac{3(1)+1}{2(1)-1}=frac{4}{1}=4, quad(4,1) in A )

( P=2, quad x=frac{3(2)+1}{2(2)-1}=frac{7}{3}, quadleft(frac{7}{3}, 2right) in A )

( P=3, quad x=frac{3(3)+1}{2(3)-1}=frac{10}{5}=2,(2,3) Leftrightarrow A )

( P=4, quad x=frac{3(4)+1}{2(4)-1}=frac{13}{7},left(frac{13}{7}, 4right) in A )

( P=5 quad x=frac{3(5)+1}{2(5)-1}=frac{16}{9},left(frac{16}{9}, 5right) in A )

( therefore quad A=left{(-1,0),(4,1),left(frac{7}{3}, 2right),(2,3),left(frac{13}{7}, 4right),left(frac{16}{9}, 5right)right} )

( A_{n} )