解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=46$$ 和公比：$$r=0.8260869565217391$$ 插入几何级数的公式：

$$a_1=46$$

$$a_2=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{2-1}=46\cdot {0.8260869565217391}^1=46\cdot 0.8260869565217391=38$$

$$a_3=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{3-1}=46\cdot {0.8260869565217391}^2=46\cdot 0.6824196597353497=31.391304347826086$$

$$a_4=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{4-1}=46\cdot {0.8260869565217391}^3=46\cdot 0.5637379797813759=25.931947069943288$$

$$a_5=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{5-1}=46\cdot {0.8260869565217391}^4=46\cdot 0.4656965919933105=21.42204323169228$$

$$a_6=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{6-1}=46\cdot {0.8260869565217391}^5=46\cdot 0.38470588034229997=17.6964704957458$$

$$a_7=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{7-1}=46\cdot {0.8260869565217391}^6=46\cdot 0.31780050984798697=14.618823453007401$$

$$a_8=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{8-1}=46\cdot {0.8260869565217391}^7=46\cdot 0.26253085596138054=12.076419374223505$$

$$a_9=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{9-1}=46\cdot {0.8260869565217391}^8=46\cdot 0.2168733157941839=9.976172526532459$$

$$a_{10}=a_1·r^{n-1}=46\cdot {0.8260869565217391}^{10-1}=46\cdot {0.8260869565217391}^9=46\cdot 0.1791562173951954=8.241186000178988$$