解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=42$$ 和公比：$$r=0.6190476190476191$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{2-1}=42\cdot {0.6190476190476191}^1=42\cdot 0.6190476190476191=26$$

$$a_3=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{3-1}=42\cdot {0.6190476190476191}^2=42\cdot 0.3832199546485261=16.095238095238095$$

$$a_4=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{4-1}=42\cdot {0.6190476190476191}^3=42\cdot 0.23723140049670666=9.96371882086168$$

$$a_5=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{5-1}=42\cdot {0.6190476190476191}^4=42\cdot 0.1468575336408184=6.1680164129143735$$

$$a_6=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{6-1}=42\cdot {0.6190476190476191}^5=42\cdot 0.09091180653955425=3.8182958746612785$$

$$a_7=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{7-1}=42\cdot {0.6190476190476191}^6=42\cdot 0.05627873738162883=2.3637069700284106$$

$$a_8=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{8-1}=42\cdot {0.6190476190476191}^7=42\cdot 0.03483921837910356=1.4632471719223494$$

$$a_9=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{9-1}=42\cdot {0.6190476190476191}^8=42\cdot 0.02156713518706411=0.9058196778566926$$

$$a_{10}=a_1·r^{n-1}=42\cdot {0.6190476190476191}^{10-1}=42\cdot {0.6190476190476191}^9=42\cdot 0.013351083687230163=0.5607455148636669$$