(4/3*(1/2)^3)/(2/9)^2= (4/3*1/8)/(4/81)=(1/6)/(4/81)=(1/6)*(81/4)=27/8=3,375
Решение:
Дано:
а1=-7
а2=-1
а3=5
Из данной последовательности найдём разность арифметической прогрессии:
d=a2-a1=-1 - (-7)=-1+7=6
или:
d=a3-a2=5- (-1)=5+1=6
91-й член арифметической прогрессии найдём по формуле:
an=a1+d(n-1)
Подставим известные нам данные:
а91=-7+6*(91-1)=-7+6*90=-7+540=533
Ответ: а91=533
1)
![log_3x\ \textgreater \ log_3(5-x)](https://tex.z-dn.net/?f=log_3x%5C+%5Ctextgreater+%5C+log_3%285-x%29)
ОДЗ:
![\left \{ {{x\ \textgreater \ 0} \atop {5-x\ \textgreater \ 0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7B5-x%5C+%5Ctextgreater+%5C+0%7D%7D+%5Cright.+)
![\left \{ {{x\ \textgreater \ 0} \atop {x\ \textless \ 5}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7Bx%5C+%5Ctextless+%5C+5%7D%7D+%5Cright.+)
![x](https://tex.z-dn.net/?f=x)
∈
![(0;5)](https://tex.z-dn.net/?f=%280%3B5%29)
![x\ \textgreater \ 5-x](https://tex.z-dn.net/?f=x%5C+%5Ctextgreater+%5C+5-x)
![x+x\ \textgreater \ 5](https://tex.z-dn.net/?f=x%2Bx%5C+%5Ctextgreater+%5C+5)
![2x\ \textgreater \ 5](https://tex.z-dn.net/?f=2x%5C+%5Ctextgreater+%5C+5)
![x\ \textgreater \ 2.5](https://tex.z-dn.net/?f=x%5C+%5Ctextgreater+%5C+2.5)
------------(2.5)-------------------
//////////////////////
----(0)--------------(5)-----------
///////////////
![x](https://tex.z-dn.net/?f=x)
∈
![(2.5;5) ](https://tex.z-dn.net/?f=%282.5%3B5%29%0A)
Ответ: целые решения: 3; 4
2)
![log_ \frac{1}{7} (2x+3)\ \textless \ log_ \frac{1}{7} (3x-2)](https://tex.z-dn.net/?f=log_+%5Cfrac%7B1%7D%7B7%7D+%282x%2B3%29%5C+%5Ctextless+%5C+log_+%5Cfrac%7B1%7D%7B7%7D+%283x-2%29)
JLP^
![\left \{ {{2x+3\ \textgreater \ 0} \atop {3x-2\ \textgreater \ 0}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2x%2B3%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7B3x-2%5C+%5Ctextgreater+%5C+0%7D%7D+%5Cright.+)
![\left \{ {{2x\ \textgreater \ -3} \atop {3x\ \textgreater \ 2}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2x%5C+%5Ctextgreater+%5C+-3%7D+%5Catop+%7B3x%5C+%5Ctextgreater+%5C+2%7D%7D+%5Cright.)
![\left \{ {{x\ \textgreater \ -1.5} \atop {x\ \textgreater \ \frac{2}{3} }} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+-1.5%7D+%5Catop+%7Bx%5C+%5Ctextgreater+%5C++%5Cfrac%7B2%7D%7B3%7D+%7D%7D+%5Cright.)
![x](https://tex.z-dn.net/?f=x)
∈
![( \frac{2}{3} ;+](https://tex.z-dn.net/?f=%28+%5Cfrac%7B2%7D%7B3%7D+%3B%2B)
∞
![)](https://tex.z-dn.net/?f=%29)
![2x+3\ \textgreater \ \ 3x-2](https://tex.z-dn.net/?f=2x%2B3%5C+%5Ctextgreater+%5C+%5C+3x-2)
![2x-3x\ \textgreater \ \ -2-3](https://tex.z-dn.net/?f=2x-3x%5C+%5Ctextgreater+%5C+%5C+-2-3)
![-x\ \textgreater \ -5](https://tex.z-dn.net/?f=-x%5C+%5Ctextgreater+%5C+-5)
![x\ \textless \ 5](https://tex.z-dn.net/?f=x%5C+%5Ctextless+%5C+5)
----------(2/3)------------------
//////////////////////
-----------------------(5)-------
//////////////////////////
![x](https://tex.z-dn.net/?f=x)
∈
![( \frac{2}{3} ;5)](https://tex.z-dn.net/?f=%28+%5Cfrac%7B2%7D%7B3%7D+%3B5%29)
Ответ: целые решения: 1; 2; 3; 4