b₃=135 b₆=5 S₅=?
b₃=b₁q²=135
b₆=b₁q⁵=5
Разделим второе уравнение на первое:
q³=1/27=(1/3)³
q=1/3
b₁*(1/3)²=135
b₁/9=135
b₁=1215
Sn=b₁*(qⁿ-1)/(q-1)
S₆=1215*((1/3)⁵-1)/((1/3)-1)=1215*((1/243)-1)/(-2/3)=1215*(-242)*3/(-2*243)=
=1215*121*3/243=1215*121/81=15*121=1815.
Ответ: S₆=1815.
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Verified answer
b₃=135 b₆=5 S₅=?
b₃=b₁q²=135
b₆=b₁q⁵=5
Разделим второе уравнение на первое:
q³=1/27=(1/3)³
q=1/3
b₁*(1/3)²=135
b₁/9=135
b₁=1215
Sn=b₁*(qⁿ-1)/(q-1)
S₆=1215*((1/3)⁵-1)/((1/3)-1)=1215*((1/243)-1)/(-2/3)=1215*(-242)*3/(-2*243)=
=1215*121*3/243=1215*121/81=15*121=1815.
Ответ: S₆=1815.