Odpowiedź:
2. ( x, 2 x + 3, 4 x + 3) - c. g.
więc (2 x + 3)² = x*( 4 x + 3)
4 x² + 12 x + 9 = 4 x² + 3 x
12 x - 3 x = - 9
9 x = - 9 / : 9
x = - 1
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Mamy ciąg ( - 1, 1, - 1)
[tex]a_n = (-1)^n[/tex] n ∈ { 1, 2, 3}
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z.3
[tex]a_1 = 2 \\a_2 = 2,5\\q = a_2 :a_1 = \frac{5}{4}[/tex]
[tex]S_{12} = a_1*\frac{1 - q^n}{1 - q}[/tex] = 2* [tex]\frac{1 - (\frac{5}{4} )^n}{1 - \frac{5}{4} }[/tex] = - 8* ( 1 - ([tex]\frac{5}{4} )^{12}[/tex]
[tex]a_n = a_1*q^{n -1}[/tex] = 2*[tex](\frac{5}{4})^{n -1}[/tex]
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z.1
[tex]a_n = 7*3^{ 1 - 3n}[/tex]
[tex]a_{n+1} = 7*3^{ 1 - 3*(n +1)}[/tex] = [tex]7*3^{ -2 - 2n}[/tex]
więc
[tex]a_{n +1} : a_n = 7*3^{ -2 - 3n} : 7*3^{ 1 -3 n} = 3^{ -2 - 3n -( 1 - 3n)} = 3^{-3} = \frac{1}{27}[/tex] = q
Jest to ciąg geometryczny.
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