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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?

Respuesta :

Janay1012
248 


windows on first floor = 52 

windows on 8th floor (52 - 6 * 7) = 10 

average windows = (52 + 10)/2 = 62/2 = 31 

8 floors * 31 average windows = 248.

Answer:

There are 248 windows on the first eight floors.

Step-by-step explanation:

As given:

The ground floor has 52 windows.

This question is based on arithmetic sequence:

a1 = 52

d = - 6 (each floor has six fewer windows than the floor below it)

[tex]a_n=a1+(n-1)d[/tex]

[tex]a_8 =a1+7d[/tex]

=> [tex]52+[7 \times (-6)][/tex]

=> [tex]52-42 =10[/tex]

We know:

[tex]S_n= n/2 \times (a1 +a _n)[/tex]

[tex]S_8 =8/2 \times(52+10)[/tex]

= 248

Therefore, there are 248 windows on the first eight floors.

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