Verified answer

ДАНО:

Геометрическая прогрессия bₙ; q= –3; S₅= –305

НАЙТИ:

b₁; b₄; S₈

РЕШЕНИЕ:

[tex] \\ sn = \frac{b1(q {}^{n} - 1)}{q - 1} \\ \\ s5 = \frac{b1(( - 3) {}^{5} - 1)}{ - 3 - 1} \\ \\ - 305 = \frac{b1( - 243 - 1)}{ - 4} \\ \\ \frac{b1 \times ( - 244)}{ - 4} = - 305 \\ \\ 61 \times b1 = - 305 \\ b1 = - 305 \div 61 \\ b1 = - 5[/tex]

[tex]bn = b1 \times q {}^{n - 1} \\ b4 = b1 \times ( - 3) {}^{4 - 1} = \\ = - 5 \times ( - 3) {}^{3} = - 5 \times ( - 27) = \\ = 135[/tex]

[tex] \\ s8 = \frac{ - 5(( - 3) {}^{8} - 1)}{ - 3 - 1} = \\ \\ = \frac{ - 5(6561 - 1)}{ - 4} = \frac{ - 5 \times 6560}{ - 4} = \\ \\ = \frac{ - 32800}{ - 4} = 8200[/tex]

ОТВЕТ: b₁= –5; b₄=135; S₈=8 200