منتديات الرياضيات العربية - عرض مشاركة واحدة

18-11-2009, 10:02 PM

السلام عليكم ،

a , b ,c are in a G.P. if b² = ac

b² = -4 x -12 = 48

$b= \pm \sqrt{48}= \pm \sqrt{16\times 3}= \pm 4\sqrt{3}$

We have two GP's

$-4 , 4\sqrt{3}, -12$

of first term a = -4 and common ratio

$r= \frac{4\sqrt{3}}{-4}= -\sqrt{3}$

${a}_{n}=a \times {r}^{n-1}= -4\times (-\sqrt{3})^{n-1}$

The second one

$-4 , - 4\sqrt{3}, -12$

of first term a = -4 and common ratio

$r= \frac{-4\sqrt{3}}{-4}= \sqrt{3}$

${a}_{n}=a \times {r}^{n-1}= -4\times (\sqrt{3})^{n-1}$