解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=69$$ 和公比：$$r=1.0869565217391304$$ 插入几何级数的公式：

$$a_1=69$$

$$a_2=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{2-1}=69\cdot {1.0869565217391304}^1=69\cdot 1.0869565217391304=75$$

$$a_3=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{3-1}=69\cdot {1.0869565217391304}^2=69\cdot 1.1814744801512287=81.52173913043478$$

$$a_4=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{4-1}=69\cdot {1.0869565217391304}^3=69\cdot 1.2842113914687268=88.61058601134215$$

$$a_5=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{5-1}=69\cdot {1.0869565217391304}^4=69\cdot 1.395881947248616=96.3158543601545$$

$$a_6=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{6-1}=69\cdot {1.0869565217391304}^5=69\cdot 1.5172629861397997=104.69114604364619$$

$$a_7=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{7-1}=69\cdot {1.0869565217391304}^6=69\cdot 1.6491988979780432=113.79472396048499$$

$$a_8=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{8-1}=69\cdot {1.0869565217391304}^7=69\cdot 1.7926074978022208=123.68991734835323$$

$$a_9=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{9-1}=69\cdot {1.0869565217391304}^8=69\cdot 1.9484864106545876=134.44556233516656$$

$$a_{10}=a_1·r^{n-1}=69\cdot {1.0869565217391304}^{10-1}=69\cdot {1.0869565217391304}^9=69\cdot 2.1179200115810732=146.13648079909404$$