解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=40$$ 和公比：$$r=0.6$$ 插入几何级数的公式：

$$a_1=40$$

$$a_2=a_1·r^{n-1}=40\cdot {0.6}^{2-1}=40\cdot {0.6}^1=40\cdot 0.6=24$$

$$a_3=a_1·r^{n-1}=40\cdot {0.6}^{3-1}=40\cdot {0.6}^2=40\cdot 0.36=14.399999999999999$$

$$a_4=a_1·r^{n-1}=40\cdot {0.6}^{4-1}=40\cdot {0.6}^3=40\cdot 0.21599999999999997=8.639999999999999$$

$$a_5=a_1·r^{n-1}=40\cdot {0.6}^{5-1}=40\cdot {0.6}^4=40\cdot 0.1296=5.183999999999999$$

$$a_6=a_1·r^{n-1}=40\cdot {0.6}^{6-1}=40\cdot {0.6}^5=40\cdot 0.07775999999999998=3.1103999999999994$$

$$a_7=a_1·r^{n-1}=40\cdot {0.6}^{7-1}=40\cdot {0.6}^6=40\cdot 0.04665599999999999=1.8662399999999995$$

$$a_8=a_1·r^{n-1}=40\cdot {0.6}^{8-1}=40\cdot {0.6}^7=40\cdot 0.027993599999999993=1.1197439999999999$$

$$a_9=a_1·r^{n-1}=40\cdot {0.6}^{9-1}=40\cdot {0.6}^8=40\cdot 0.016796159999999994=0.6718463999999997$$

$$a_{10}=a_1·r^{n-1}=40\cdot {0.6}^{10-1}=40\cdot {0.6}^9=40\cdot 0.010077695999999997=0.4031078399999999$$