解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=100$$ 和公比：$$r=0.6$$ 插入几何级数的公式：

$$a_1=100$$

$$a_2=a_1·r^{n-1}=100\cdot {0.6}^{2-1}=100\cdot {0.6}^1=100\cdot 0.6=60$$

$$a_3=a_1·r^{n-1}=100\cdot {0.6}^{3-1}=100\cdot {0.6}^2=100\cdot 0.36=36$$

$$a_4=a_1·r^{n-1}=100\cdot {0.6}^{4-1}=100\cdot {0.6}^3=100\cdot 0.21599999999999997=21.599999999999998$$

$$a_5=a_1·r^{n-1}=100\cdot {0.6}^{5-1}=100\cdot {0.6}^4=100\cdot 0.1296=12.959999999999999$$

$$a_6=a_1·r^{n-1}=100\cdot {0.6}^{6-1}=100\cdot {0.6}^5=100\cdot 0.07775999999999998=7.775999999999998$$

$$a_7=a_1·r^{n-1}=100\cdot {0.6}^{7-1}=100\cdot {0.6}^6=100\cdot 0.04665599999999999=4.665599999999999$$

$$a_8=a_1·r^{n-1}=100\cdot {0.6}^{8-1}=100\cdot {0.6}^7=100\cdot 0.027993599999999993=2.799359999999999$$

$$a_9=a_1·r^{n-1}=100\cdot {0.6}^{9-1}=100\cdot {0.6}^8=100\cdot 0.016796159999999994=1.6796159999999993$$

$$a_{10}=a_1·r^{n-1}=100\cdot {0.6}^{10-1}=100\cdot {0.6}^9=100\cdot 0.010077695999999997=1.0077695999999996$$