解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=200$$ 和公比：$$r=1.025$$ 插入几何级数的公式：

$$a_1=200$$

$$a_2=a_1·r^{n-1}=200\cdot {1.025}^{2-1}=200\cdot {1.025}^1=200\cdot 1.025=204.99999999999997$$

$$a_3=a_1·r^{n-1}=200\cdot {1.025}^{3-1}=200\cdot {1.025}^2=200\cdot 1.050625=210.12499999999997$$

$$a_4=a_1·r^{n-1}=200\cdot {1.025}^{4-1}=200\cdot {1.025}^3=200\cdot 1.0768906249999997=215.37812499999993$$

$$a_5=a_1·r^{n-1}=200\cdot {1.025}^{5-1}=200\cdot {1.025}^4=200\cdot 1.1038128906249995=220.76257812499992$$

$$a_6=a_1·r^{n-1}=200\cdot {1.025}^{6-1}=200\cdot {1.025}^5=200\cdot 1.1314082128906244=226.2816425781249$$

$$a_7=a_1·r^{n-1}=200\cdot {1.025}^{7-1}=200\cdot {1.025}^6=200\cdot 1.15969341821289=231.93868364257798$$

$$a_8=a_1·r^{n-1}=200\cdot {1.025}^{8-1}=200\cdot {1.025}^7=200\cdot 1.1886857536682123=237.73715073364247$$

$$a_9=a_1·r^{n-1}=200\cdot {1.025}^{9-1}=200\cdot {1.025}^8=200\cdot 1.2184028975099173=243.68057950198346$$

$$a_{10}=a_1·r^{n-1}=200\cdot {1.025}^{10-1}=200\cdot {1.025}^9=200\cdot 1.2488629699476652=249.77259398953305$$