๋ถ€๋ถ„์˜ ํ•ฉ์ด ์ฃผ์–ด์ง„ ๋“ฑ๋น„์ˆ˜์—ด

ex)

๋“ฑ๋น„์ˆ˜์—ด ${a_n}$์˜ ์ฒซ์งธํ•ญ๋ถ€ํ„ฐ ์ œnํ•ญ๊นŒ์ง€์˜ ํ•ฉ $S_n$์— ๋Œ€ํ•˜์—ฌ $S_n=30, S_{2n}=50$์ผ ๋•Œ, $S_{3n}$์˜ ๊ฐ’์„ ๊ตฌํ•˜์‹œ์˜ค.

- ์Žˆ ์ˆ˜ํ•™ I / 146p 970๋ฒˆ ๋ฌธ์ œ

$
\begin{aligned}\dfrac{a\left( r^{2n}-1\right) }{r-1}=50\\
\dfrac{a\left( r^{n}-1\right) }{r-1}=30\\
\dfrac{\dfrac{a\left( r^{2n}-1\right) }{r-1}}{\dfrac{a\left( r^{n}-1\right) }{r-1}}=\dfrac{5}{3}\\
\dfrac{r^{2n}-1^{2}}{r^{n}-1}=\dfrac{\left( r^{n}+1\right) \left( r^{n}-1\right) }{r^{n}-1}=r^{n}+1=\dfrac{5}{3}\\
r^{n}=\dfrac{2}{3}\\
\dfrac{a}{r-1}\times \left( -\dfrac{1}{3}\right) =30\\
\dfrac{a}{r-1}=-90\\
S_{3n}=\dfrac{a\left( r^{3n}-1\right) }{r-1}=-90\times \left( \dfrac{8}{27}-1\right) \\
=-90x\left( -\dfrac{19}{27}\right) =\dfrac{190}{3}\end{aligned}
$