Answer:
looks like A, first answer, is correct when using n such that it names what value of the sequence to use like a1 = 4 and so on.
Step-by-step explanation:
First we would need to find the portion of the gymnasium to the blueprint to do that please do this:
88/5.5 = 16
The length divided by the blueprint's length
Since we know that the gymnasium is 16 times the blueprint, to find the width divide 16 to 76:
76/16 = 4.75
The width divided by the 16 times
The width of the blueprint is 4.75 inches
![\green{\large\underline{\sf{Solution-}}}](https://tex.z-dn.net/?f=%20%5Cgreen%7B%5Clarge%5Cunderline%7B%5Csf%7BSolution-%7D%7D%7D)
<u>Given expression is </u>
![\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} }](https://tex.z-dn.net/?f=%5Crm%20%3A%5Clongmapsto%5C%3A%5Cdfrac%7B5%20%5Ctimes%20%20%7B25%7D%5E%7Bn%20%2B%201%7D%20%20-%2025%20%5Ctimes%20%20%7B5%7D%5E%7B2n%7D%20%7D%7B5%20%5Ctimes%20%20%7B5%7D%5E%7B2n%20%2B%203%7D%20%20-%20%20%7B25%7D%5E%7Bn%20%2B%201%7D%20%7D%20)
can be rewritten as
![\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} }](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B5%20%5Ctimes%20%20%7B%20%7B%285%7D%5E%7B2%7D%20%29%7D%5E%7Bn%20%2B%201%7D%20%20-%20%20%7B5%7D%5E%7B2%7D%20%20%5Ctimes%20%20%7B5%7D%5E%7B2n%7D%20%7D%7B5%20%5Ctimes%20%20%7B5%7D%5E%7B2n%20%2B%203%7D%20%20-%20%20%7B%28%20%7B5%7D%5E%7B2%7D%20%29%7D%5E%7Bn%20%2B%201%7D%20%7D%20)
We know,
![\purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\](https://tex.z-dn.net/?f=%20%5Cpurple%7B%5Crm%20%3A%5Clongmapsto%5C%3A%5Cboxed%7B%5Ctt%7B%20%20%7B%28%20%7Bx%7D%5E%7Bm%7D%20%29%7D%5E%7Bn%7D%20%20%5C%3A%20%3D%20%5C%3A%20%20%20%7Bx%7D%5E%7Bmn%7D%7D%7D%7D%20%5C%5C%20)
And
![\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\](https://tex.z-dn.net/?f=%20%5Cpurple%7B%5Crm%20%3A%5Clongmapsto%5C%3A%5Cboxed%7B%5Ctt%7B%20%5C%3A%20%20%5C%3A%20%20%20%7Bx%7D%5E%7Bm%7D%20%5Ctimes%20%20%7Bx%7D%5E%7Bn%7D%20%3D%20%20%7Bx%7D%5E%7Bm%20%2B%20n%7D%20%5C%3A%20%7D%7D%7D%20%5C%5C%20)
So, using this identity, we
![\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} }](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B5%20%5Ctimes%20%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%20-%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%7D%7B%7B5%7D%5E%7B2n%20%2B%203%20%2B%201%7D%20%20-%20%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%7D%20)
![\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} }](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B%7B5%7D%5E%7B2n%20%2B%202%20%2B%201%7D%20%20-%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%7D%7B%7B5%7D%5E%7B2n%20%2B%204%7D%20%20-%20%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%7D%20)
can be further rewritten as
![\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} }](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B%7B5%7D%5E%7B2n%20%2B%202%20%2B%201%7D%20%20-%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%7D%7B%7B5%7D%5E%7B2n%20%2B%202%20%2B%202%7D%20%20-%20%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%7D%20)
![\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)}](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%285%20-%201%29%7D%7B%20%7B5%7D%5E%7B2n%20%2B%202%7D%20%28%20%7B5%7D%5E%7B2%7D%20%20-%201%29%7D%20)
![\rm \: = \: \dfrac{4}{25 - 1}](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B4%7D%7B25%20-%201%7D%20)
![\rm \: = \: \dfrac{4}{24}](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B4%7D%7B24%7D%20)
![\rm \: = \: \dfrac{1}{6}](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%20%3D%20%20%5C%3A%20%5Cdfrac%7B1%7D%7B6%7D%20)
<u>Hence, </u>
![\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}](https://tex.z-dn.net/?f=%5Crm%20%3A%5Clongmapsto%5C%3A%5Cboxed%7B%5Ctt%7B%20%5Cdfrac%7B5%20%5Ctimes%20%20%7B25%7D%5E%7Bn%20%2B%201%7D%20%20-%2025%20%5Ctimes%20%20%7B5%7D%5E%7B2n%7D%20%7D%7B5%20%5Ctimes%20%20%7B5%7D%5E%7B2n%20%2B%203%7D%20%20-%20%20%7B25%7D%5E%7Bn%20%2B%201%7D%20%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B6%7D%20%7D%7D)
ANSWER:
15
32
31
10
23
6.5
35
4.8
63
66
200
72
Solution:
Say you have a triangle that is 2.5 by 1
The Number that comes first is the base and there’s only one bass and there’s two sides in those size are 1 so 1×2 is 2+2.5=4.5 so all you’re doing is adding up all the sides together on any shape