Question

Решите пожалуйста
знайдіть b1 якщо S4=13 q=-2/3

Answer 1

$\displaystyle\bf\\q=-\frac{2}{3} \\\\S_{4} =13\\\\b_{1}=?\\\\\\S_{4} =\frac{b_{1} \cdot(1-q^{4} )}{1-q} \\\\\\13=\frac{b_{1} \cdot\bigg(1-\bigg(-\dfrac{2}{3} \bigg)^{4} \bigg)}{1-\bigg(-\dfrac{2}{3} \bigg)} \\\\\\13=\frac{b_{1} \cdot\bigg(1-\dfrac{16}{81} \bigg)}{1+\dfrac{2}{3} } \\\\\\13=\frac{b_{1} \cdot\dfrac{65}{81} }{\dfrac{5}{3} } \\\\\\13=b_{1} \cdot\dfrac{13}{27}\\\\\\b_{1} =13:\frac{13}{27}=13\cdot\frac{27}{13} =27 \\\\\\Otvet: \ b_{1} =27$