+120 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?
It is a simple arithmetic series:
1st.term=52
Number od terms=8
Common difference = -6
You just sum the series up and you will get: 248 windows.
+26367 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?
arithmetic series:
\( a_1 = 52,~d = +6\)
formular:
\(a_n = a_1+(n-1)\cdot d\)
\(\begin{array}{rcll} a_n~?\\ a_n &=& 52+(n-1)\cdot 6 \\ a_n &=& 52+6n-6 \\ \mathbf{a_n} & \mathbf{=} & \mathbf{46+6n} \end{array}\)
sum:
\(\begin{array}{rcll} s_n~? \\ s_n &=& \left( \frac{a_1+a_n}{2} \right) \cdot n \\ s_n &=& \left( \frac{ 52+(46+6n) }{2} \right)\cdot n \\ \mathbf{s_n} & \mathbf{=} & \mathbf{\left( \frac{ 98+6n }{2}\right)\cdot n} \end{array}\)
total windows on the first eight floors?
n=8
\(\begin{array}{rcll} s_8~? \\ s_8 & = & \left( \frac{ 98+6\cdot8 }{2}\right)\cdot 8 \\ s_8 & = & \left( \frac{ 98+48 }{2}\right)\cdot 8 \\ s_8 & = & \left( \frac{ 146 }{2}\right)\cdot 8 \\ s_8 & = & 146 \cdot 4 \\ \mathbf{s_8} & \mathbf{=} & \mathbf{584} \\ \end{array}\)
On the first eight floors are total 584 windows.
