解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=60$$ 和公比：$$r=0.9$$ 插入几何级数的公式：

$$a_1=60$$

$$a_2=a_1·r^{n-1}=60\cdot {0.9}^{2-1}=60\cdot {0.9}^1=60\cdot 0.9=54$$

$$a_3=a_1·r^{n-1}=60\cdot {0.9}^{3-1}=60\cdot {0.9}^2=60\cdot 0.81=48.6$$

$$a_4=a_1·r^{n-1}=60\cdot {0.9}^{4-1}=60\cdot {0.9}^3=60\cdot 0.7290000000000001=43.74000000000001$$

$$a_5=a_1·r^{n-1}=60\cdot {0.9}^{5-1}=60\cdot {0.9}^4=60\cdot 0.6561=39.366$$

$$a_6=a_1·r^{n-1}=60\cdot {0.9}^{6-1}=60\cdot {0.9}^5=60\cdot 0.5904900000000001=35.4294$$

$$a_7=a_1·r^{n-1}=60\cdot {0.9}^{7-1}=60\cdot {0.9}^6=60\cdot 0.531441=31.886460000000003$$

$$a_8=a_1·r^{n-1}=60\cdot {0.9}^{8-1}=60\cdot {0.9}^7=60\cdot 0.4782969000000001=28.697814000000005$$

$$a_9=a_1·r^{n-1}=60\cdot {0.9}^{9-1}=60\cdot {0.9}^8=60\cdot 0.4304672100000001=25.828032600000007$$

$$a_{10}=a_1·r^{n-1}=60\cdot {0.9}^{10-1}=60\cdot {0.9}^9=60\cdot 0.3874204890000001=23.245229340000005$$