解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=42$$ 和公比：$$r=1.7142857142857142$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{2-1}=42\cdot {1.7142857142857142}^1=42\cdot 1.7142857142857142=72$$

$$a_3=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{3-1}=42\cdot {1.7142857142857142}^2=42\cdot 2.9387755102040813=123.42857142857142$$

$$a_4=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{4-1}=42\cdot {1.7142857142857142}^3=42\cdot 5.037900874635568=211.59183673469386$$

$$a_5=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{5-1}=42\cdot {1.7142857142857142}^4=42\cdot 8.636401499375259=362.72886297376084$$

$$a_6=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{6-1}=42\cdot {1.7142857142857142}^5=42\cdot 14.805259713214728=621.8209079550186$$

$$a_7=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{7-1}=42\cdot {1.7142857142857142}^6=42\cdot 25.38044522265382=1065.9786993514604$$

$$a_8=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{8-1}=42\cdot {1.7142857142857142}^7=42\cdot 43.50933466740654=1827.3920560310748$$

$$a_9=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{9-1}=42\cdot {1.7142857142857142}^8=42\cdot 74.58743085841121=3132.6720960532707$$

$$a_{10}=a_1·r^{n-1}=42\cdot {1.7142857142857142}^{10-1}=42\cdot {1.7142857142857142}^9=42\cdot 127.86416718584779=5370.295021805608$$