\ \left \{ {{b_1+b_1\cdot q+b_1\cdot q^2=168,} \atop {b_1\cdot q^3+b_1\cdot q^4+b_1\cdot q^5=21;}} \right. \ ==> \ \left \{ {{b_1\cdot\left(1+q+q^2\right)=168,} \atop {b_1\cdot\left(q^3+q^4+q^5\right)=21;}} \right.\\ \left \{ {{b_1\cdot\left(1+q+q^2\right)=168,} \atop {b_1\cdot q^3\left(1+q+q^2\right)=21;}} \right. \\ b_1\cdot\left(1+q+q^2\right)=168\ ==> \\ b_1\cdot q^3\left(1+q+q^2\right)=21\\ q^3\cdot168=21\\ " alt=" b_n=b_1\cdot q^{n-1};\\ \left \{ {{b_1+b_2+b_3=168}, \atop {b_4+b_5+b_6=21};} \right. \ ==> \ \left \{ {{b_1+b_1\cdot q+b_1\cdot q^2=168,} \atop {b_1\cdot q^3+b_1\cdot q^4+b_1\cdot q^5=21;}} \right. \ ==> \ \left \{ {{b_1\cdot\left(1+q+q^2\right)=168,} \atop {b_1\cdot\left(q^3+q^4+q^5\right)=21;}} \right.\\ \left \{ {{b_1\cdot\left(1+q+q^2\right)=168,} \atop {b_1\cdot q^3\left(1+q+q^2\right)=21;}} \right. \\ b_1\cdot\left(1+q+q^2\right)=168\ ==> \\ b_1\cdot q^3\left(1+q+q^2\right)=21\\ q^3\cdot168=21\\ " align="absmiddle" class="latex-formula">
b_1=\frac{168}{1+\frac12+\frac14}=;\\ b_1=\frac{168}{\frac{4+2+1}{4}}=\frac{672}{7}=96;\\ b_n=b_1\cqrt q^{n-1};\\[tex] b_1=96;\\ b_2=96\cdot \frac12=48;\\ b_3=96\cdot\frac14=24;\\ b_4=96\cdot\frac18=12;\\ b_5=96\cdot\frac1{16}=6;\\ b_6=96\cdot\frac1{32}=3;\\ " alt=" q^3=\frac{21}{168}=\frac{3\cdot7}{7\cdot24}=\frac{3}{24}=\frac18;\\ q=\sqrt[3]{\frac18}=\frac12;\\ b_1(1+q+q^2)=168==>b_1=\frac{168}{1+\frac12+\frac14}=;\\ b_1=\frac{168}{\frac{4+2+1}{4}}=\frac{672}{7}=96;\\ b_n=b_1\cqrt q^{n-1};\\[tex] b_1=96;\\ b_2=96\cdot \frac12=48;\\ b_3=96\cdot\frac14=24;\\ b_4=96\cdot\frac18=12;\\ b_5=96\cdot\frac1{16}=6;\\ b_6=96\cdot\frac1{32}=3;\\ " align="absmiddle" class="latex-formula">
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