Question

B2=2 b1+b3=4 b8-?
Геометрическая прогрессия ​

Answer 1

$b_{2}=2 \ \Rightarrow \ b_{1}\cdot q=2\\\\b_{1}+b_{3}=4\\\\b_{1}+b_{1} \cdot q^{2}=4\\\\b_{1}+\underbrace{b_{1}\cdot q}_{2}\cdot q= 4\\\\b_{1} +2q=4\\\\b_{1}=4-2q\\\\\left \{ {{b_{1}\cdot q=2 } \atop {b_{1}=4-2q }} \right.\\\\\left \{ {{(4-2q)\cdot q=2} \atop {b_{1}=4-2q }} \right. \\\\\left \{ {{4q-2q^{2} -2=0} \atop {b_{1}=4-2q }} \right.\\\\\left \{ {{q^{2}-2q+1=0 } \atop {b_{1}=4-2q }} \right.$

$\left \{ {{(q-1)^{2}=0 } \atop {b_{1}=4-2q }} \right. \\\\\left \{ {{q-1=0} \atop {b_{1}=4-2q }} \right.\\\\\left \{ {{q=1} \atop {b_{1}=4-2\cdot 1 }} \right.\\\\\left \{ {{q=1} \atop {b_{1} =2}} \right. \\\\b_{8}=b_{1}\cdot q^{7} =2\cdot 1^{7}=2 \\\\\boxed{b_{8}=2}$