解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=1,440$$ 和公比：$$r=1.09375$$ 插入几何级数的公式：

$$a_1=1440$$

$$a_2=a_1·r^{n-1}=1440\cdot {1.09375}^{2-1}=1440\cdot {1.09375}^1=1440\cdot 1.09375=1575$$

$$a_3=a_1·r^{n-1}=1440\cdot {1.09375}^{3-1}=1440\cdot {1.09375}^2=1440\cdot 1.1962890625=1722.65625$$

$$a_4=a_1·r^{n-1}=1440\cdot {1.09375}^{4-1}=1440\cdot {1.09375}^3=1440\cdot 1.308441162109375=1884.1552734375$$

$$a_5=a_1·r^{n-1}=1440\cdot {1.09375}^{5-1}=1440\cdot {1.09375}^4=1440\cdot 1.431107521057129=2060.7948303222656$$

$$a_6=a_1·r^{n-1}=1440\cdot {1.09375}^{6-1}=1440\cdot {1.09375}^5=1440\cdot 1.5652738511562347=2253.994345664978$$

$$a_7=a_1·r^{n-1}=1440\cdot {1.09375}^{7-1}=1440\cdot {1.09375}^6=1440\cdot 1.7120182747021317=2465.3063155710697$$

$$a_8=a_1·r^{n-1}=1440\cdot {1.09375}^{8-1}=1440\cdot {1.09375}^7=1440\cdot 1.8725199879554566=2696.4287826558575$$

$$a_9=a_1·r^{n-1}=1440\cdot {1.09375}^{9-1}=1440\cdot {1.09375}^8=1440\cdot 2.0480687368262807=2949.218981029844$$

$$a_{10}=a_1·r^{n-1}=1440\cdot {1.09375}^{10-1}=1440\cdot {1.09375}^9=1440\cdot 2.2400751809037445=3225.708260501392$$