解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=88$$ 和公比：$$r=1.0909090909090908$$ 插入几何级数的公式：

$$a_1=88$$

$$a_2=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{2-1}=88\cdot {1.0909090909090908}^1=88\cdot 1.0909090909090908=96$$

$$a_3=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{3-1}=88\cdot {1.0909090909090908}^2=88\cdot 1.190082644628099=104.7272727272727$$

$$a_4=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{4-1}=88\cdot {1.0909090909090908}^3=88\cdot 1.298271975957926=114.24793388429748$$

$$a_5=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{5-1}=88\cdot {1.0909090909090908}^4=88\cdot 1.4162967010450103=124.6341096919609$$

$$a_6=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{6-1}=88\cdot {1.0909090909090908}^5=88\cdot 1.5450509465945563=135.96448330032095$$

$$a_7=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{7-1}=88\cdot {1.0909090909090908}^6=88\cdot 1.6855101235576977=148.3248908730774$$

$$a_8=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{8-1}=88\cdot {1.0909090909090908}^7=88\cdot 1.8387383166083975=161.80897186153896$$

$$a_9=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{9-1}=88\cdot {1.0909090909090908}^8=88\cdot 2.005896345390979=176.51887839440613$$

$$a_{10}=a_1·r^{n-1}=88\cdot {1.0909090909090908}^{10-1}=88\cdot {1.0909090909090908}^9=88\cdot 2.1882505586083405=192.56604915753397$$