解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=580$$ 和公比：$$r=1.05$$ 插入几何级数的公式：

$$a_1=580$$

$$a_2=a_1·r^{n-1}=580\cdot {1.05}^{2-1}=580\cdot {1.05}^1=580\cdot 1.05=609$$

$$a_3=a_1·r^{n-1}=580\cdot {1.05}^{3-1}=580\cdot {1.05}^2=580\cdot 1.1025=639.45$$

$$a_4=a_1·r^{n-1}=580\cdot {1.05}^{4-1}=580\cdot {1.05}^3=580\cdot 1.1576250000000001=671.4225000000001$$

$$a_5=a_1·r^{n-1}=580\cdot {1.05}^{5-1}=580\cdot {1.05}^4=580\cdot 1.2155062500000002=704.9936250000002$$

$$a_6=a_1·r^{n-1}=580\cdot {1.05}^{6-1}=580\cdot {1.05}^5=580\cdot 1.2762815625000004=740.2433062500002$$

$$a_7=a_1·r^{n-1}=580\cdot {1.05}^{7-1}=580\cdot {1.05}^6=580\cdot 1.3400956406250004=777.2554715625002$$

$$a_8=a_1·r^{n-1}=580\cdot {1.05}^{8-1}=580\cdot {1.05}^7=580\cdot 1.4071004226562505=816.1182451406253$$

$$a_9=a_1·r^{n-1}=580\cdot {1.05}^{9-1}=580\cdot {1.05}^8=580\cdot 1.477455443789063=856.9241573976566$$

$$a_{10}=a_1·r^{n-1}=580\cdot {1.05}^{10-1}=580\cdot {1.05}^9=580\cdot 1.5513282159785162=899.7703652675394$$