Odpowiedź:
[tex]a_1, a_2, a_3,a_4, ... , a_{n-1}, a_n[/tex], ... - ciąg geometryczny
Mamy
[tex]S_{np} = \frac{a_1}{1 - q^2} = 16[/tex] ⇒ [tex]a_1 = 16*( 1 - q^2)[/tex]
[tex]S_p = \frac{a_2}{1 - q^2} = 4[/tex]
więc [tex]S_{np} = 4 S_p[/tex]
[tex]\frac{a_1}{1 - q^2} = 4*\frac{a_1 q}{1 - q^2}[/tex] / : [tex]a_1[/tex]
[tex]\frac{1}{1 -q^2} = \frac{4 q}{1 - q^2}[/tex]
[tex]4 q = 1[/tex]
[tex]q = \frac{1}{4}[/tex] oraz [tex]a_1 = 16*( 1 - (\frac{1}{4})^2) = 16 - 1 = 15[/tex]
zatem[tex]S_5 = a_1*\frac{1 - q^5}{1 - q} =[/tex] 15* [tex]\frac{1 - \frac{1}{1024} }{1 - \frac{1}{4} } =[/tex] 19 [tex]\frac{251}{256}[/tex]
Szczegółowe wyjaśnienie: