Знайти перший член і знаменник геометричної прогресії ( ) bn , якщо b6=96, b9=768.. Created by dimarepyakh. algebra-ru

B₆ = 96b₉ = 768Найти q; b₁bn = b₁qⁿ⁻¹b₆ = b₁*q⁵b₉ = b₁*q⁸b₁q⁵ = 96b₁q⁸ = 768 b₆ = b₁*q⁵b₁ = b₆ : q⁵b₁ = 96 : 2⁵ b₁ = 96 : 32 b₁ = 3 Ответ: b₁ = 3; q = 2.

Знайти перший член і знаменник геометричної прогресії ( ) bn , якщо b6=96, b9=76...

dimarepyakh @dimarepyakh

August 2022 1 7 Report

Знайти перший член і знаменник геометричної прогресії
( ) bn , якщо b6=96, b9=768.

Answers & Comments

kolobok1431

Verified answer

B₆ = 96
b₉ = 768
Найти q; b₁

bn = b₁qⁿ⁻¹

b₆ = b₁*q⁵
b₉ = b₁*q⁸

b₁q⁵ = 96
b₁q⁸ = 768

$\frac{ b_{1} q^{8} }{ b_{1} q^{5} } = \frac{768}{96}$
$q^{3}=8$
$q^{3}= 2^{3}$
$q=2$

b₆ = b₁*q⁵
b₁ = b₆ : q⁵
b₁ = 96 : 2⁵
b₁ = 96 : 32
b₁ = 3
Ответ: b₁ = 3; q = 2.

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