Question

Найдите сумму первых 6 членов геометрической прогрессии если b6=25 , b8=9.

Answer 1

$b_6=25,; b_8=9\\ frac{b_8}{b_6} = frac{b_1q^7}{b_1q^5} =q^2; ; to ; ; q^2= frac{9}{25} =(frac{3}{5})^2; ; to \\q=pm frac{3}{5}\\b_1=frac{b_6}{q^5}=frac{25}{pm (frac{3}{5})^5}=pm frac{5^7}{3^5}=pm frac{3125}{243}\\Esli; b_1=-frac{3125}{243},; to; q=-frac{3}{5}.\\Esli; b_1=+frac{3125}{243},; to; q=+frac{3}{5}\\S_6= frac{b_1-b_6q}{1-q}\\1)S_6 = frac{frac{3125}{243}-25cdot frac{3}{5}}{1-frac{3}{5}} = frac{5cdot 3125-25cdot 3cdot 243}{243cdot 2} =$

$= frac{-2600}{486} =-5 frac{170}{243} \\2); ; S_6= frac{-frac{3125}{243}+frac{3}{5}cdot 25}{1+frac{3}{5}}= frac{2600}{1944}=1frac{656}{1944}$