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The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors?

Verified Answer :

HomertheGenius

The ground floor:  52 windows.
We will use the arithmetic sequence:
a 1 = 52
d = - 6
a n = a 1 + ( n - 1 ) d
a 8 = a 1 + 7 d
a 8 = 52 + 7 ( - 6 ) = 52 - 42 = 10
S n = n/2 ( a 1 + a n )
S 8 = 8/2 ( 52 + 10 ) = 4 62 = 248
Answer:
There are 248 windows on the first eight floors.