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：$$r=1.619047619047619$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {1.619047619047619}^{2-1}=42\cdot {1.619047619047619}^1=42\cdot 1.619047619047619=68$$

$$a_3=a_1·r^{n-1}=42\cdot {1.619047619047619}^{3-1}=42\cdot {1.619047619047619}^2=42\cdot 2.621315192743764=110.09523809523809$$

$$a_4=a_1·r^{n-1}=42\cdot {1.619047619047619}^{4-1}=42\cdot {1.619047619047619}^3=42\cdot 4.244034121585142=178.24943310657596$$

$$a_5=a_1·r^{n-1}=42\cdot {1.619047619047619}^{5-1}=42\cdot {1.619047619047619}^4=42\cdot 6.871293339709278=288.59432026778967$$

$$a_6=a_1·r^{n-1}=42\cdot {1.619047619047619}^{6-1}=42\cdot {1.619047619047619}^5=42\cdot 11.12495112143407=467.24794710023093$$

$$a_7=a_1·r^{n-1}=42\cdot {1.619047619047619}^{7-1}=42\cdot {1.619047619047619}^6=42\cdot 18.011825625178968=756.4966762575167$$

$$a_8=a_1·r^{n-1}=42\cdot {1.619047619047619}^{8-1}=42\cdot {1.619047619047619}^7=42\cdot 29.162003393146904=1224.80414251217$$

$$a_9=a_1·r^{n-1}=42\cdot {1.619047619047619}^{9-1}=42\cdot {1.619047619047619}^8=42\cdot 47.21467216033308=1983.0162307339895$$

$$a_{10}=a_1·r^{n-1}=42\cdot {1.619047619047619}^{10-1}=42\cdot {1.619047619047619}^9=42\cdot 76.44280254530118=3210.5977069026494$$