解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=73$$ 和公比：$$r=6.8493150684931505$$ 插入几何级数的公式：

$$a_1=73$$

$$a_2=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{2-1}=73\cdot {6.8493150684931505}^1=73\cdot 6.8493150684931505=500$$

$$a_3=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{3-1}=73\cdot {6.8493150684931505}^2=73\cdot 46.91311690748733=3424.657534246575$$

$$a_4=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{4-1}=73\cdot {6.8493150684931505}^3=73\cdot 321.32271854443377=23456.558453743666$$

$$a_5=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{5-1}=73\cdot {6.8493150684931505}^4=73\cdot 2200.8405379755736=160661.35927221688$$

$$a_6=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{6-1}=73\cdot {6.8493150684931505}^5=73\cdot 15074.250260106668=1100420.2689877867$$

$$a_7=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{7-1}=73\cdot {6.8493150684931505}^6=73\cdot 103248.28945278541=7537125.130053335$$

$$a_8=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{8-1}=73\cdot {6.8493150684931505}^7=73\cdot 707180.0647451055=51624144.7263927$$

$$a_9=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{9-1}=73\cdot {6.8493150684931505}^8=73\cdot 4843699.073596613=353590032.3725527$$

$$a_{10}=a_1·r^{n-1}=73\cdot {6.8493150684931505}^{10-1}=73\cdot {6.8493150684931505}^9=73\cdot 33176021.05203159=2421849536.798306$$