Question

30 балов. Геометртческая прогрессия:
b5 = 10 , q = - 2/3 , S7 - ?

Answer 1

$b_5=10;$
$q=-\frac{2}{3}$
$b_n=b_1q^{n-1}$
$b_1=b_5:q^{5-1}$

$b_1=10:(-\frac{2}{3})^{4})=10:\frac{16}{81}=$
$10*\frac{81}{16}=\frac{405}{8}$

$S_n=b_1*\frac{q^n-1}{q-1}$
$S_7=\frac{405}{8}*\frac{(-\frac{2}{3})^7-1}{-\frac{2}{3}-1}=$
$\frac{405}{8}*\frac{\frac{128}{2187}+1}{\frac{5}{3}}=$
$\frac{405}{8}*\frac{128+2187}{2187}*\frac{3}{5}=$
$\frac{5*81*2315*3}{8*81*3*9*5}=$
$\frac{2315}{72}$