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KiraPolina
@KiraPolina
May 2021
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Алгебра 9 класс. Геометрическая прогрессия. Решите сколько сможете,пожалуйста!
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sangers1959
Verified answer
1.
a₁=64 q=-1/4 a₇=?
a₇=a₁q⁶=64*(-1/4)⁶=4³*(-4)⁻⁶=4³⁻⁶=4⁻³=1/64.
2.
b₇=256 q=-3 b₁-?
b₇=b₁*(-2)⁶=256
b₁=256/(-2)⁶=256/64
b₁=4.
3.
b₁=-4 q=2 S₅-?
S₅=b₁*(qⁿ=1)/(q-1)=-4*(2⁵-1)/(2-1)=-4*31=-124
S₅=-124.
4.
a₁=3 q=-2 S₄-?
S₄=3*((-2)⁴-1)/(-2-1)=5*15/(-3)=75/(-3)=-25
S₄=-25.
5.
3√3; 3; √3 ...
b₁=3√3
q=3/(3√3)=1/√3=√3/3≈0,58
q=√3/3
S=b₁/(1-q)=3√3/(1-√3/3)=3√3/((3-√3)/3)=9√3/(3-√3)=
=9√3*(3+√3)/((3-√3)(3+√3))=9√3*(3+√3)/(9-3)=(27√3+27)/6=4,5*(√3+1).
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Answers & Comments
Verified answer
1.a₁=64 q=-1/4 a₇=?
a₇=a₁q⁶=64*(-1/4)⁶=4³*(-4)⁻⁶=4³⁻⁶=4⁻³=1/64.
2.
b₇=256 q=-3 b₁-?
b₇=b₁*(-2)⁶=256
b₁=256/(-2)⁶=256/64
b₁=4.
3.
b₁=-4 q=2 S₅-?
S₅=b₁*(qⁿ=1)/(q-1)=-4*(2⁵-1)/(2-1)=-4*31=-124
S₅=-124.
4.
a₁=3 q=-2 S₄-?
S₄=3*((-2)⁴-1)/(-2-1)=5*15/(-3)=75/(-3)=-25
S₄=-25.
5.
3√3; 3; √3 ...
b₁=3√3
q=3/(3√3)=1/√3=√3/3≈0,58
q=√3/3
S=b₁/(1-q)=3√3/(1-√3/3)=3√3/((3-√3)/3)=9√3/(3-√3)=
=9√3*(3+√3)/((3-√3)(3+√3))=9√3*(3+√3)/(9-3)=(27√3+27)/6=4,5*(√3+1).