Odpowiedź:
a)
[tex]a_1=4\\a_2=4\cdot q\\a_3=4\cdot q\cdot q=4q^2\\4q^{2} =16/:4\\q^{2} =4/\sqrt{} \\q=2\quad \lor\quad q=-2\\a_2=4\cdot2\quad \quad a_2=4\cdot(-2)\\\underline{a_2=8\quad \lor\quad a_2=-8}[/tex]
b)
[tex]a_3=4\\a_6=32\\a_n=a_1q^{n-1}\\a_3=a_1q^2\\a_6=a_1q^5\\\displaystyle \frac{a_6}{a_3} =\frac{a_1q^5}{a_1q^2} =q^3\quad \frac{a_6}{a_3}=\frac{32}{4} =8\quad \Rightarrow q^3=8\quad \Rightarrow q=2\\a_3=a_1q^{2} =a_1\cdot2^2=4a_1\\4a_1=4/:4\\a_1=1\\S_n=a_1\frac{1-q^n}{1-q} \\S_8=1\cdot\frac{1-2^8}{1-2} =2^{8} -1=256-1=\underline{255}[/tex]
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
Odpowiedź:
a)
[tex]a_1=4\\a_2=4\cdot q\\a_3=4\cdot q\cdot q=4q^2\\4q^{2} =16/:4\\q^{2} =4/\sqrt{} \\q=2\quad \lor\quad q=-2\\a_2=4\cdot2\quad \quad a_2=4\cdot(-2)\\\underline{a_2=8\quad \lor\quad a_2=-8}[/tex]
b)
[tex]a_3=4\\a_6=32\\a_n=a_1q^{n-1}\\a_3=a_1q^2\\a_6=a_1q^5\\\displaystyle \frac{a_6}{a_3} =\frac{a_1q^5}{a_1q^2} =q^3\quad \frac{a_6}{a_3}=\frac{32}{4} =8\quad \Rightarrow q^3=8\quad \Rightarrow q=2\\a_3=a_1q^{2} =a_1\cdot2^2=4a_1\\4a_1=4/:4\\a_1=1\\S_n=a_1\frac{1-q^n}{1-q} \\S_8=1\cdot\frac{1-2^8}{1-2} =2^{8} -1=256-1=\underline{255}[/tex]