解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=168$$ 和公比：$$r=1.0714285714285714$$ 插入几何级数的公式：

$$a_1=168$$

$$a_2=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{2-1}=168\cdot {1.0714285714285714}^1=168\cdot 1.0714285714285714=180$$

$$a_3=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{3-1}=168\cdot {1.0714285714285714}^2=168\cdot 1.1479591836734693=192.85714285714283$$

$$a_4=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{4-1}=168\cdot {1.0714285714285714}^3=168\cdot 1.2299562682215743=206.6326530612245$$

$$a_5=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{5-1}=168\cdot {1.0714285714285714}^4=168\cdot 1.317810287380258=221.39212827988334$$

$$a_6=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{6-1}=168\cdot {1.0714285714285714}^5=168\cdot 1.411939593621705=237.20585172844642$$

$$a_7=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{7-1}=168\cdot {1.0714285714285714}^6=168\cdot 1.512792421737541=254.14912685190689$$

$$a_8=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{8-1}=168\cdot {1.0714285714285714}^7=168\cdot 1.6208490232902226=272.3026359127574$$

$$a_9=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{9-1}=168\cdot {1.0714285714285714}^8=168\cdot 1.7366239535252384=291.75282419224004$$

$$a_{10}=a_1·r^{n-1}=168\cdot {1.0714285714285714}^{10-1}=168\cdot {1.0714285714285714}^9=168\cdot 1.8606685216341838=312.5923116345429$$