Question

Sa se determine primu termen si ratia progresiei geometric (b indice n) stiind ca b indice 4 supra b indice 1 este egal cu 8 si S indice 8 este egal cu 255

Answer 1

$\frac{ b_{4} }{b1} = 8\ \textless \ =\ \textgreater \ \frac{b1*q^{3}}{b1} =8=\ \textgreater \ 8 b_{1} =b1q^{3} |: b_{1} =\ \textgreater \ q^{3}=8=\ \textgreater \ q=2$
$S8= \frac{ b_{1}(q^{8}-1) }{q-1} \ \textless \ =\ \textgreater \ 255=b_{1}q^{8}-b_{1}\ \textless \ =\ \textgreater \ 255=b_{1}*2^{8}-b1 \ \textless \ =\ \textgreater$=>$255=256b_{1}-b1 \ \textless \ =\ \textgreater \ 255=255b_{1}|:255=\ \textgreater \ b_{1}=1$
$b_{1}=1; q=2$