解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=123$$ 和公比：$$r=1.146341463414634$$ 插入几何级数的公式：

$$a_1=123$$

$$a_2=a_1·r^{n-1}=123\cdot {1.146341463414634}^{2-1}=123\cdot {1.146341463414634}^1=123\cdot 1.146341463414634=141$$

$$a_3=a_1·r^{n-1}=123\cdot {1.146341463414634}^{3-1}=123\cdot {1.146341463414634}^2=123\cdot 1.3140987507436048=161.6341463414634$$

$$a_4=a_1·r^{n-1}=123\cdot {1.146341463414634}^{4-1}=123\cdot {1.146341463414634}^3=123\cdot 1.5064058849987663=185.28792385484826$$

$$a_5=a_1·r^{n-1}=123\cdot {1.146341463414634}^{5-1}=123\cdot {1.146341463414634}^4=123\cdot 1.7268555267059027=212.40322978482604$$

$$a_6=a_1·r^{n-1}=123\cdot {1.146341463414634}^{6-1}=123\cdot {1.146341463414634}^5=123\cdot 1.9795660915896933=243.4866292655323$$

$$a_7=a_1·r^{n-1}=123\cdot {1.146341463414634}^{7-1}=123\cdot {1.146341463414634}^6=123\cdot 2.2692586903589165=279.11881891414674$$

$$a_8=a_1·r^{n-1}=123\cdot {1.146341463414634}^{8-1}=123\cdot {1.146341463414634}^7=123\cdot 2.601345327972416=319.96547534060716$$

$$a_9=a_1·r^{n-1}=123\cdot {1.146341463414634}^{9-1}=123\cdot {1.146341463414634}^8=123\cdot 2.9820300101147206=366.78969124411066$$

$$a_{10}=a_1·r^{n-1}=123\cdot {1.146341463414634}^{10-1}=123\cdot {1.146341463414634}^9=123\cdot 3.418424645741265=420.46623142617557$$