解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=1,904$$ 和公比：$$r=1.0625$$ 插入几何级数的公式：

$$a_1=1904$$

$$a_2=a_1·r^{n-1}=1904\cdot {1.0625}^{2-1}=1904\cdot {1.0625}^1=1904\cdot 1.0625=2023$$

$$a_3=a_1·r^{n-1}=1904\cdot {1.0625}^{3-1}=1904\cdot {1.0625}^2=1904\cdot 1.12890625=2149.4375$$

$$a_4=a_1·r^{n-1}=1904\cdot {1.0625}^{4-1}=1904\cdot {1.0625}^3=1904\cdot 1.199462890625=2283.77734375$$

$$a_5=a_1·r^{n-1}=1904\cdot {1.0625}^{5-1}=1904\cdot {1.0625}^4=1904\cdot 1.2744293212890625=2426.513427734375$$

$$a_6=a_1·r^{n-1}=1904\cdot {1.0625}^{6-1}=1904\cdot {1.0625}^5=1904\cdot 1.354081153869629=2578.1705169677734$$

$$a_7=a_1·r^{n-1}=1904\cdot {1.0625}^{7-1}=1904\cdot {1.0625}^6=1904\cdot 1.4387112259864807=2739.3061742782593$$

$$a_8=a_1·r^{n-1}=1904\cdot {1.0625}^{8-1}=1904\cdot {1.0625}^7=1904\cdot 1.5286306776106358=2910.5128101706505$$

$$a_9=a_1·r^{n-1}=1904\cdot {1.0625}^{9-1}=1904\cdot {1.0625}^8=1904\cdot 1.6241700949613005=3092.419860806316$$

$$a_{10}=a_1·r^{n-1}=1904\cdot {1.0625}^{10-1}=1904\cdot {1.0625}^9=1904\cdot 1.7256807258963818=3285.696102106711$$