Odpowiedź:
z. 1
(an) : 2,4,8,16,32, ...
więc a1 = 2 q = 2
Sn = a1*[tex]\frac{1 - q^n}{1 - q}[/tex] = 2* [tex]\frac{1 - 2^n}{1 - 2}[/tex] = 2*( 2^n - 1) = 2*2^n - 2 = 2 046
2*2^n = 2 048 / : 2
2^n = 1 024
n = 10
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z.2
a3 = 6 a6 = 162
Mamy
a6 : a3 = ( a1*q^5 : a1*q^2) = q³ = 162 : 6 = 27
q³ = 27 = 3³
q = 3
====
a1 = a3: q² = 6 : 9 = [tex]\frac{2}{3}[/tex]
zatem
an = a1*q^(n-1) = [tex]\frac{2}{3}[/tex] * 3^{n -1} = [tex]\frac{2}{9}[/tex] *3^n
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Szczegółowe wyjaśnienie:
