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Dana2554326
@Dana2554326
July 2022
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b3=3,6, a b5=32,4. Найдите сумму пяти первых членов этой прогрессии, если все члены прогрессии положительны
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oganesbagoyan
Verified answer
B₃ = 3,6 ;
b₅
=32,4 ;
q >0 .
----
S
₅ -?
S₅ = b₁(q
⁵
-1) / (q -1).
{ b
₁q² =3,6 ; b₁q⁴ =32,4.⇔ { q² =32,4/3,6 ; b₁q² =3,6. ⇔
{ q² =9 ; b₁*9 =3,6. ⇔ || т|к. q >0 || { q =3 ; b₁ = 3,6 /9. ⇔ { b₁ =0,4 ;q =3
.
S₅ =b₁(q⁵ -1) / (q -1) =0,4 (3⁵ -1) / (3 -1) =0,4*242 /2 =0,4*121 = 48,4.
ответ : 48,4 .
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Answers & Comments
Verified answer
B₃ = 3,6 ;b₅ =32,4 ;
q >0 .
----
S₅ -?
S₅ = b₁(q⁵ -1) / (q -1).
{ b₁q² =3,6 ; b₁q⁴ =32,4.⇔ { q² =32,4/3,6 ; b₁q² =3,6. ⇔
{ q² =9 ; b₁*9 =3,6. ⇔ || т|к. q >0 || { q =3 ; b₁ = 3,6 /9. ⇔ { b₁ =0,4 ;q =3 .
S₅ =b₁(q⁵ -1) / (q -1) =0,4 (3⁵ -1) / (3 -1) =0,4*242 /2 =0,4*121 = 48,4.
ответ : 48,4 .