Let {x} and [x] denote the fractional part of x and the greatest integer ≤ x respectively of a real number x. If ∫_0^n {x} d x, ∫_0^n [x] d x and 10(…

Let $\displaystyle \{x\}$ and $\displaystyle [x]$ denote the fractional part of $\displaystyle x$ and the greatest integer $\displaystyle \leq x$ respectively of a real number $\displaystyle x$. If $\displaystyle \int_0^{\mathrm{n}}\{x\} \mathrm{d} x, \int_0^{\mathrm{n}}[x] \mathrm{d} x$ and $\displaystyle 10\left(\mathrm{n}^2-\mathrm{n}\right)$, $\displaystyle (\mathrm{n} \in \mathrm{N}, \mathrm{n}>1)$ are three consecutive terms of a G.P., then n is equal to \_\_\_\_.