解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=20$$ 和公比：$$r=0.9$$ 插入几何级数的公式：

$$a_1=20$$

$$a_2=a_1·r^{n-1}=20\cdot {0.9}^{2-1}=20\cdot {0.9}^1=20\cdot 0.9=18$$

$$a_3=a_1·r^{n-1}=20\cdot {0.9}^{3-1}=20\cdot {0.9}^2=20\cdot 0.81=16.200000000000003$$

$$a_4=a_1·r^{n-1}=20\cdot {0.9}^{4-1}=20\cdot {0.9}^3=20\cdot 0.7290000000000001=14.580000000000002$$

$$a_5=a_1·r^{n-1}=20\cdot {0.9}^{5-1}=20\cdot {0.9}^4=20\cdot 0.6561=13.122$$

$$a_6=a_1·r^{n-1}=20\cdot {0.9}^{6-1}=20\cdot {0.9}^5=20\cdot 0.5904900000000001=11.809800000000001$$

$$a_7=a_1·r^{n-1}=20\cdot {0.9}^{7-1}=20\cdot {0.9}^6=20\cdot 0.531441=10.628820000000001$$

$$a_8=a_1·r^{n-1}=20\cdot {0.9}^{8-1}=20\cdot {0.9}^7=20\cdot 0.4782969000000001=9.565938000000001$$

$$a_9=a_1·r^{n-1}=20\cdot {0.9}^{9-1}=20\cdot {0.9}^8=20\cdot 0.4304672100000001=8.609344200000002$$

$$a_{10}=a_1·r^{n-1}=20\cdot {0.9}^{10-1}=20\cdot {0.9}^9=20\cdot 0.3874204890000001=7.748409780000002$$