ОДЗ: x>0
![Замена: [tex]a=log_{0,5}x](https://tex.z-dn.net/?f=%C2%A0+%D0%97%D0%B0%D0%BC%D0%B5%D0%BD%D0%B0%3A+%5Btex%5Da%3Dlog_%7B0%2C5%7Dx)
a²+a-2≤0
(a+2)(a-1)≤0
+ - +
________[-2]_____________[1]_________
a∈[-2;1]
<span>\left \{ {log_{0,5}x \geq -2} \atop {log_{0,5}x \leq 1}} \right. =\ \textgreater \ \left \{ {{log_{0,5}x \geq log_{0,5}4} \atop {log_{0,5}x \leq log_{0,5}0,5}} \right.\; \; \; \; \; \; 0\ \textless \ 0,5\ \textless \ 1\\\\ \left \{ {{x \leq 4} \atop {x \geq 0,5}} \right. [/tex]
</span>
Ответ: [0,5;4]
1)a1=11 U a7=35⇒d=(a7-a1)/6=(35-11)/6=24/6=4
a4=a1+3d=11+3*4=11+12=23
b1=38, bn=13 U b4=23
d=(b4-b1)/3=(23-38)/3=-15/3=-5
bn=b1+d(n-1)
38-5(n-1)=23
5(n-1)=38-23=15
n-1=15/5=3
n=3+1=4
2a)a1=6 d=5 an=96
an=a1+d(n-1)=6+5(n-1)=96
5(n-1)=96-6=90
n-1=90/5=18
n=18+1=19
S19=(2*6+18*5)*19/2=(12+90)*19/2=102*19/2=51*19=969
б)a1=1 d=1
S(от 1 до 99)=S99=(2+98)*100/2=5000
b1=5 d=5 bn=95⇒5+5(n-1)=95⇒5(n-1)=95-5=90⇒n-1=90/5=18⇒n=19
S19=(10+5*18)*19/2=50*19=950
S99-S19=5000-950=4050
Sn=(a1+an)2⋅n
Данные подставляем в формулу:
(а1+6) :2 *18 = 306
(а1+6) *9 = 306
а1+6=34
а1 = 28
Ответ: значение а1 = 28.
