解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=55$$ 和公比：$$r=1.0909090909090908$$ 插入几何级数的公式：

$$a_1=55$$

$$a_2=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{2-1}=55\cdot {1.0909090909090908}^1=55\cdot 1.0909090909090908=59.99999999999999$$

$$a_3=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{3-1}=55\cdot {1.0909090909090908}^2=55\cdot 1.190082644628099=65.45454545454544$$

$$a_4=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{4-1}=55\cdot {1.0909090909090908}^3=55\cdot 1.298271975957926=71.40495867768593$$

$$a_5=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{5-1}=55\cdot {1.0909090909090908}^4=55\cdot 1.4162967010450103=77.89631855747557$$

$$a_6=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{6-1}=55\cdot {1.0909090909090908}^5=55\cdot 1.5450509465945563=84.9778020627006$$

$$a_7=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{7-1}=55\cdot {1.0909090909090908}^6=55\cdot 1.6855101235576977=92.70305679567338$$

$$a_8=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{8-1}=55\cdot {1.0909090909090908}^7=55\cdot 1.8387383166083975=101.13060741346186$$

$$a_9=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{9-1}=55\cdot {1.0909090909090908}^8=55\cdot 2.005896345390979=110.32429899650384$$

$$a_{10}=a_1·r^{n-1}=55\cdot {1.0909090909090908}^{10-1}=55\cdot {1.0909090909090908}^9=55\cdot 2.1882505586083405=120.35378072345873$$