Odpowiedź:
[tex]a)\\a_1=128\\a_2=64\\a_3=32\\64=128*q /:128\\\frac{64}{128}=q\\\underline{q=\frac12}\\\\\underline{a_n=128*(\frac12)^{n-1}}\\\\a_7=128*(\frac12)^6\\a_7=128*\frac1{64}\\\underline{a_7=2}[/tex]
[tex]b)\\\\a_1=\frac1{16}\\a_2=\frac14\\a_3=1\\1=\frac14*q /*4\\\underline{q=4}\\\\\underline{a_n=\frac1{16}*4^{n-1}}\\\\a_7=\frac1{16}*4^6\\a_7=4^{-2}*4^6\\a_7=4^4\\\underline{a_7=256}[/tex]
[tex]c)\\\\a_1=\frac1{243}\\a_2=-\frac1{81}\\a_3=\frac1{27}\\\\\frac1{27}=-\frac1{81}*q /*(-81)\\-\frac{81}{27}=q\\\underline{q=-3}\\\\\underline{a_n=\frac1{243}*(-3)^{n-1}}\\\\a_7=\frac1{243}*(-3)^6\\a_7=3^{-5}*3^6\\a_7=3^1\\\underline{a_7=3}[/tex]
[tex]d)\\\\a_1=\frac{625}{256}=\frac{5^4}{4^4}=(\frac54)^4\\a_2=\frac{125}{64}=\frac{5^3}{4^3}=(\frac54)^3\\a_3=\frac{25}{16}=(\frac54)^2\\\\(\frac54)^2=(\frac54)^3*q /:(\frac54)^3\\(\frac54)^2:(\frac54)^3=q\\q=(\frac54)^{-1}\\\underline{q=\frac45}\\\\\underline{a_n=\frac{625}{256}*(\frac45)^{n-1}}\\\\a_7=\frac{625}{256}*(\frac45)^6\\a_7=(\frac{5}4)^4*(\frac45)^6\\a_7=(\frac45)^{-4}*(\frac45)^6\\a_7=(\frac45)^2\\\underline{a_7=\frac{16}{25}}[/tex]
[tex]e)\\\\a_1=\sqrt2\\a_2=-2\\a_3=2\sqrt2\\\\-2=\sqrt2*q /:\sqrt2\\\frac{-2}{\sqrt2}=q\\q=-\frac{2\sqrt2}2\\\underline{q=-\sqrt2}\\\\\underline{a_n=\sqrt2*(-\sqrt2)^{n-1}}\\\\a_7=\sqrt2*(-\sqrt2)^6\\a_7=2^{\frac12}*(2^{\frac12})^6\\a_7=2^{\frac12}*2^{\frac62}\\a_7=2^{\frac72}\\a_7=\sqrt{2^7}\\a_7=\sqrt{2^6*2}\\\underline{a_7=8\sqrt2}[/tex]
[tex]f)\\\\a_1=\frac29\\a_2=\frac13\\a_3=\frac12\\\\\frac12=\frac13*q /*3\\\underline{q=\frac32}\\\\\underline{a_n=\frac29*(\frac32)^{n-1}}\\\\a_7=\frac29*(\frac32)^6\\a_7=\frac2{3^2}*\frac{3^6}{2^6}\\a_7=\frac1{1}*\frac{3^4}{2^5}\\\underline{a_7=\frac{81}{32}}\\[/tex]
Szczegółowe wyjaśnienie:
[tex]\text{Wzor na n-ty wyraz ciagu geometrycznego}\\a_n=a_1*q^{n-1}[/tex]
