a_(3)=a_(1)+2d
4=a_(1)+2*(-5)
a_(1)=14
a_(5)=a_(1)+4d=14+4*(-5)=-8
2)
{a_(4)-a_(3)=6
{a_(4)+a_(3)=10
Склалываем
2a_(4)=16
[b]a_(4)=8[/b]
d=a_(4)-a_(3)=6
a_(4)=a_(3)+d ⇒ [b]a_(3)[/b]=a_(4)-d=[b]2[/b]
a_(2)=a_(3)-d=2-6=-4
a_(1)=a_(2)-d=-4-6=-10
a_(10)=a_(1)+9d=-10+9*6=44
S_(10)=(a_(1)+a_(10))*10/2=(-10+44)*10/2=[b]170[/b]
3)
b_(1)=1/3
b_(2)=1
q=b_(2)/b_(1)=3
b_(n)=b_(1)*q^(n-1)
b_(n)=(1/3)*3^(n-1)
[b]b_(n)=3^(n-2)[/b]
4)
b_(6)=b_(1)*q^5
200=b_(1)*10^(5)
b_(1)=200/10^5=2/1000=0,002
S_(6)=[m]\frac{b_{1}\cdot (q^{n}-1)}{q-1}=\frac{0,002\cdot (10^{6}-1)}{10-1}=\frac{0,002\cdot 999999}{9}=\frac{222222}{1000}=222,222[/m]