Prologue: Principles of Problem Solving - Problems - Page 4: 3

$427$ $f(x)=3x+1$

Each time a cut is made, $3$ extra pieces are formed. The first cut made gave $4$ pieces. So we can define the equation to be $f(x)=4+3(x-1)$ for $x$ cuts, simplified to $f(x)=3x+1$. Using this equation, we can solve the first part of the problem. Plug in $142$ to get $f(142)=3(142)+1$, simplify to get $f(142)=427$.