The lowest term is
.
Solution:
Given expression is ![50\times\frac{3}{8}](https://tex.z-dn.net/?f=50%5Ctimes%5Cfrac%7B3%7D%7B8%7D)
<u>To reduce this term to the lowest term:</u>
![$50\times\frac{3}{8}=\frac{50}{1}\times\frac{3}{8}](https://tex.z-dn.net/?f=%2450%5Ctimes%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B50%7D%7B1%7D%5Ctimes%5Cfrac%7B3%7D%7B8%7D)
Multiply the numerator and denominator.
![$50\times\frac{3}{8}=\frac{150}{8}](https://tex.z-dn.net/?f=%2450%5Ctimes%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B150%7D%7B8%7D)
Now, divide the numerator and denominator by the greatest common factor.
Here 150 and 8 both have common factor 2.
So, divide numerator and denominator by 2.
![$=\frac{150\div2}{8\div2}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B150%5Cdiv2%7D%7B8%5Cdiv2%7D)
![$=\frac{75}{4}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B75%7D%7B4%7D)
![$50\times\frac{3}{8}=\frac{75}{4}](https://tex.z-dn.net/?f=%2450%5Ctimes%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B75%7D%7B4%7D)
Hence the lowest term is
.
Answer:
8
Step-by-step explanation:
There are 4 people that are 27 and 4 people that are 29. Both are <em>older</em> than 26.
By iteratively substituting, we have
![a_n = a_{n-1} + n](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn-1%7D%20%2B%20n)
![a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)](https://tex.z-dn.net/?f=a_%7Bn-1%7D%20%3D%20a_%7Bn-2%7D%20%2B%20%28n%20-%201%29%20%5Cimplies%20a_n%20%3D%20a_%7Bn-2%7D%20%2B%20n%20%2B%20%28n%20-%201%29)
![a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)](https://tex.z-dn.net/?f=a_%7Bn-2%7D%20%3D%20a_%7Bn-3%7D%20%2B%20%28n%20-%202%29%20%5Cimplies%20a_n%20%3D%20a_%7Bn-3%7D%20%2B%20n%20%2B%20%28n%20-%201%29%20%2B%20%28n%20-%202%29)
and the pattern continues down to the first term
,
![a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn%20-%20%28n%20-%201%29%7D%20%2B%20n%20%2B%20%28n%20-%201%29%20%2B%20%28n%20-%202%29%20%2B%20%5Ccdots%20%2B%20%28n%20-%20%28n%20-%202%29%29)
![\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)](https://tex.z-dn.net/?f=%5Cimplies%20a_n%20%3D%20a_1%20%2B%20%5Cdisplaystyle%20%5Csum_%7Bk%3D0%7D%5E%7Bn-2%7D%20%28n%20-%20k%29)
![\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k](https://tex.z-dn.net/?f=%5Cimplies%20a_n%20%3D%20%5Cdisplaystyle%20n%20%5Csum_%7Bk%3D0%7D%5E%7Bn-2%7D%201%20-%20%5Csum_%7Bk%3D0%7D%5E%7Bn-2%7D%20k)
Recall the formulas
![\displaystyle \sum_{n=1}^N 1 = N](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bn%3D1%7D%5EN%201%20%3D%20N)
![\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum_%7Bn%3D1%7D%5EN%20n%20%3D%20%5Cfrac%7BN%28N%2B1%29%7D2)
It follows that
![a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2](https://tex.z-dn.net/?f=a_n%20%3D%20n%20%28n%20-%202%29%20-%20%5Cdfrac%7B%28n-2%29%28n-1%29%7D2)
![\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1](https://tex.z-dn.net/?f=%5Cimplies%20a_n%20%3D%20%5Cdfrac12%20n%5E2%20%2B%20%5Cdfrac12%20n%20-%201)
![\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Ba_n%20%3D%20%5Cdfrac%7B%28n%2B2%29%28n-1%29%7D2%7D)
Answer:
for the trapezoid it is 336
Step-by-step explanation: