Odpowiedź:
1701
Szczegółowe wyjaśnienie:
Wzór ciągu geometrycznego: [tex]a_{n}=a_{1}*q^{n-1}[/tex]
Trzeci wyraz ciągu [tex]a_{3}[/tex] = 7, a [tex]a_{5}[/tex] = 63
[tex]a_{3} = a_{1}*q^{2} \\a_{5}=a_{1}*q^{4}[/tex]
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[tex]7 = a_{1}*q^{2} \\63=a_{1}*q^{4}[/tex]
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[tex]a_{1}=\frac{7}{q^{2} }\\a_{1}=\frac{63}{q^{4} }[/tex]
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[tex]\frac{7}{q^{2} }=\frac{63}{q^{4} }[/tex]
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[tex]7q^{4}=63q^{2} /:q^2\\7q^{2} =63\\q^{2} =9\\ q=3[/tex]
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[tex]a_{8}=a_{5}*q^{3} \\a_{8}=63*3^{3}=63*27=1701[/tex]
