Question

Найдите первый член прогрессии bn, если b4−b2=−24 и b4−b3=−6.

Answer 1

$\displaystyle\bf\\\left \{ {{b_{4} -b_{2} =-24} \atop {b_{4} -b_{3} =-6}} \right. \\\\\\\left \{ {{b_{1} \cdot q{3} -b_{1}\cdot q ^{2} =-6} \atop {b_{1} \cdot q^{3} -b_{1} \cdot q =-24}} \right. \\\\\\\left \{ {{b_{1}q^{2} (q-1)=-6 } \atop {b_{1} q(q^{2} -1)=-24}} \right. \\\\\\:\left \{ {{b_{1}q^{2} (q-1)=-6 } \atop {b_{1} q(q -1)(q+1)=-24}} \right.\\--------------\\\frac{q}{q+1} =\frac{1}{4} \\\\4q=q+1\\\\3q=1\\\\q=\frac{1}{3}$

$\displaystyle\bf\\b_{1} =-\frac{6}{q^{2} (q-1)}=-\frac{6}{(\frac{1}{3} )^{2} \cdot(\frac{1}{3} -1)} =\frac{6}{\frac{1}{9} \cdot\frac{2}{3} } =\frac{6\cdot27}{2} =81\\\\\\Otvet:b_{1} =81$