Question

Sa se determine primii doi termeni ai progresiei geometrice (bn) daca :
b9=768,b11=3072

vreau va rog si formula de calcul...
multumesc mult

Answer 1

$b_{n} = \sqrt{ b_{n-1}* b_{n+1} } \\ b_{n} = b_{1} q^{n-1} \\ b_{10} = \sqrt{ b_{9}* b_{11} }= \sqrt{768*3072} = \sqrt{2359296} =1536 \\ q= \frac{ b_{10}}{ b_{9} } = \frac{1536}{768} =2 \\ b_{10} = b_{1} q^{9} =\ \textgreater \ b_{1} = \frac{ b_{10} }{ q^{9} } = \frac{1536}{512} =3 \\ b_{2} =b_{1}q^{1}=3*2=6$