|[3a-b]*[a-2b]| = | [3a,a] - [3a,2b] - [b, a] +[b,2b]| =
= |3*<u>0</u> - (6)*<u>[</u>a,b] - [b,a] +2*<u>0</u>| = | - (6)*<u>[</u>a,b] + [a,b] | =
= | - (5)*<u>[</u>a,b] | =|-5*|a| *|b|*sin(π/2) | = | -5*3*4*1| = |-60| = 60
<u>( </u>в решении <u> 0</u> обозначен нулевой вектор) ,
1)
a1=-16
d=a2-a1=-10-(-16)=-10+16=6
s17=(a1+a17)*17/2=(a1+a1+16*d)*17/2=(2a1+16d)*17/2=2(a1+8d)*17/2=(a1+8d)*17=(-16+8*6)*17=(-16*48)*17=32*17=544
an=2+5n
Свойство арифметической прогрессии:
![\frac{a_{n-1}+a_{n+1}}{2}=a_{n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba_%7Bn-1%7D%2Ba_%7Bn%2B1%7D%7D%7B2%7D%3Da_%7Bn%7D)
Подставим и упростим:
![\frac{(2+5(n-1))+(2+5(n+1))}{2}=2+5n](https://tex.z-dn.net/?f=%5Cfrac%7B%282%2B5%28n-1%29%29%2B%282%2B5%28n%2B1%29%29%7D%7B2%7D%3D2%2B5n)
![\frac{2+5n-5+2+5n+5}{2}=2+5n](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B5n-5%2B2%2B5n%2B5%7D%7B2%7D%3D2%2B5n)
![\frac{4+10n}{2}=2+5n](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B10n%7D%7B2%7D%3D2%2B5n)
![\frac{2(2+5n)}{2}=2+5n](https://tex.z-dn.net/?f=%5Cfrac%7B2%282%2B5n%29%7D%7B2%7D%3D2%2B5n)
ЧТД
A7=a1+6d=-10
a1-6=-10
a1=-4
a9=-4+8*(-1)=-12
S9=(a1+a9)*9/2=-16*9/2=-72