解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=53$$ 和公比：$$r=0.8679245283018868$$ 插入几何级数的公式：

$$a_1=53$$

$$a_2=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{2-1}=53\cdot {0.8679245283018868}^1=53\cdot 0.8679245283018868=46$$

$$a_3=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{3-1}=53\cdot {0.8679245283018868}^2=53\cdot 0.7532929868280528=39.924528301886795$$

$$a_4=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{4-1}=53\cdot {0.8679245283018868}^3=53\cdot 0.6538014602658572=34.65147739409043$$

$$a_5=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{5-1}=53\cdot {0.8679245283018868}^4=53\cdot 0.5674503240043288=30.07486717222943$$

$$a_6=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{6-1}=53\cdot {0.8679245283018868}^5=53\cdot 0.49250405479620996=26.10271490419913$$

$$a_7=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{7-1}=53\cdot {0.8679245283018868}^6=53\cdot 0.42745634944576716=22.65518652062566$$

$$a_8=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{8-1}=53\cdot {0.8679245283018868}^7=53\cdot 0.37099985046236394=19.66299207450529$$

$$a_9=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{9-1}=53\cdot {0.8679245283018868}^8=53\cdot 0.3219998702126178=17.065993121268743$$

$$a_{10}=a_1·r^{n-1}=53\cdot {0.8679245283018868}^{10-1}=53\cdot {0.8679245283018868}^9=53\cdot 0.2794715854675551=14.811994029780418$$