wzór
[tex] a_{n} = a_{1} \times {q}^{n - 1} [/tex]
[tex]14 = a_{1} \times q \\ 28 = a_{1} \times {q}^{2} \\ \\ q = \frac{14}{a_{1}} \\ 28 = a_{1} \times ( \frac{14}{a_{1}} {)}^{2} \\ \\ q = \frac{14}{a_{1}} \\ 28 = a_{1} \times \frac{196}{ {a_{1}}^{2} } \\ \\ q = \frac{14}{a_{1}} \\ 28 = \frac{196}{a_{1}} \\ \\ q = \frac{14}{a_{1}} \\ a_{1} = 7 \\ \\ q = \frac{14}{7} \\ a_{1} = 7 \\ \\ q = 2 \\ a_{1} = 7[/tex]
[tex]a_{4} = 7 \times {2}^{4 - 1} = 7 \times {2}^{3} = 7 \times 8 = 56[/tex]
b)
[tex]S_{15} = 7 \times \frac{1 - {2}^{15} }{1 - 2} \\ S_{15} = 7 \times \frac{1 -32768}{ - 1} \\ S_{15} =7 \times \frac{ - 32767}{ - 1} \\ S_{15} = 7 \times 32767 =229369[/tex]
