Ответ: S₇=127.

Объяснение: q>1      S₇=?

[tex]\displaystyle\\\left \{ {{b_4+b_5=24} \atop {b_6-b_3=24}} \right. \ \ \ \ \ \ \left \{ {{b_1q^3+b_1q^4=24 } \atop {b_1q^5-b_1q^3=24 \right. \ \ \ \ \ \ \left \{ {b_1q^3*(1+q)=24\ \ \ \ (1)} \atop {b_1q^3*(q^2-1)=24\ \ \ \ (2)}} \right. .\\\\[/tex]

Разделим уравнение (1) на уравнение (2):

[tex]\displaystyle\\\frac{b_1q^3*(1+q)}{b_1q^3*(q^2-1)} =\frac{24}{24}\\\\ \frac{1+q}{q^2-1}=1\\\\1+q=q^2-1\\\\q+1=(q+1)*(q-1)\ |:(q+1)\ \ \ (q\neq -1)\\\\1=q-1\\\\q=2.\\\\b_1*2^3*(1+2)=24\\\\24b_1=24\ |:24\\\\b_1=1\\\\S_7=1*\frac{2^7-1}{2-1} =128-1=127.[/tex]