# Question #72fd4

May 31, 2015

We have an arithmetic sequence :

${u}_{1} = 52$
${u}_{n + 1} = {u}_{n} - 6$

$\implies {u}_{n} = 52 + \left(n - 1\right) \cdot \left(- 6\right) = 58 - 6 n$,

where ${u}_{n}$ gives you the number of windows in a given floor $n$
(n = 1 = ground floor).

The sum of the windows for $n$ floors is given by :

${s}_{n} = {u}_{1} + {u}_{2} + {u}_{3} + \ldots + {u}_{n} = n \cdot \frac{{u}_{1} + {u}_{n}}{2}$.

If $n = 8$ :

${s}_{8} = 8 \cdot \frac{52 + 58 - 6 \cdot 8}{2} = 8 \cdot \frac{62}{2} = 8 \cdot 31 = 248$.