IMAS 2017–2018 Junior Round 2 Question 14

Let $a$, $b$, $c$ and $d$ be four positive integers such that $\frac{b}{a}$, $\frac{c}{b}$, $\frac{d}{c}$ are simplified fractions and $\frac{b}{a}+\frac{c}{b}+\frac{d}{c}$ is an integer. Prove that $d\ge a-1$.