\(\displaystyle{ a _{2}+a _{4}=10}\)
\(\displaystyle{ a _{3}-a _{2}=2
a _{1}=?}\)
\(\displaystyle{ q=?}\)
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Ciąg geometryczny
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arecek
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- Posty: 283
- Rejestracja: 26 sty 2007, o 22:11
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Ciąg geometryczny
\(\displaystyle{ a_{2} + a_{2} q^{2} = 10}\)
\(\displaystyle{ a_{2}q - a_{2} = 2}\)
\(\displaystyle{ a_{2}(q^{2} + 1) = 10}\)
\(\displaystyle{ a_{2}(q - 1) = 2}\)
\(\displaystyle{ \frac{q^{2} + 1}{q-1} = 5}\)
\(\displaystyle{ \frac{q^{2} + 1}{q-1} - \frac{5q-5}{q-1} = 0}\)
\(\displaystyle{ \frac{q^{2} - 5q + 6}{q-1} = 0}\)
\(\displaystyle{ q = 2 \ v \ q = 3}\)
\(\displaystyle{ 1 \ 2 \ 4 \ 8}\)
v
\(\displaystyle{ \frac{1}{3}\ 1 \ 3 \ 9}\)
\(\displaystyle{ a_{2}q - a_{2} = 2}\)
\(\displaystyle{ a_{2}(q^{2} + 1) = 10}\)
\(\displaystyle{ a_{2}(q - 1) = 2}\)
\(\displaystyle{ \frac{q^{2} + 1}{q-1} = 5}\)
\(\displaystyle{ \frac{q^{2} + 1}{q-1} - \frac{5q-5}{q-1} = 0}\)
\(\displaystyle{ \frac{q^{2} - 5q + 6}{q-1} = 0}\)
\(\displaystyle{ q = 2 \ v \ q = 3}\)
\(\displaystyle{ 1 \ 2 \ 4 \ 8}\)
v
\(\displaystyle{ \frac{1}{3}\ 1 \ 3 \ 9}\)