Question

Aflati b1 si q din urmatoarele relatii ale progresiei geometrice:

b4=-54 , b7=1458

Answer 1

Explicație pas cu pas:

$\left \{ {{b_{4} = b_{1} \cdot q^{4-1}} \atop {b_{7} = b_{1} \cdot q^{7-1}}} \right. \iff \left \{ { { - 54 = b_{1} \cdot q^{3}} \atop {1458 = b_{1} \cdot q^{6}}} \right.$

$\left \{ { {b_{1}} = - \frac{54}{{q}^{3}} \atop {1458 = \left( - \frac{54}{{q}^{3}} \right) \cdot q^{6}}} \right. \iff \left \{ { {b_{1}} = - \frac{54}{{q}^{3}} \atop { {q}^{3} = - \frac{1458}{54} }} \right.$

$\left \{ { {q^{3}} = - \frac{54}{b_{1}} \atop {1458 = b_{1} \cdot \frac{ {54}^{2} }{b_{1}^{2}}}} \right. \iff \left \{ { {q^{3}} = - \frac{54}{b_{1}} \atop {b_{1} = \frac{ {54}^{2} }{1458}}} \right.$

$\left \{ { {b_{1}} = - \frac{54}{{q}^{3}} \atop { {q}^{3} = - 27 }} \right. \iff \left \{ { {b_{1}} = - \frac{54}{{q}^{3}} \atop { {q}^{3} = - {3}^{3} }} \right.$

$\left \{ { {b_{1}} = - \frac{54}{ - 27} \atop { {q}^{3} = - {3}^{3} }} \right.\iff \left \{ { {b_{1}} = 2 \atop { q = - 3}} \right.$