解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=10$$ 和公比：$$r=0.6$$ 插入几何级数的公式：

$$a_1=10$$

$$a_2=a_1·r^{n-1}=10\cdot {0.6}^{2-1}=10\cdot {0.6}^1=10\cdot 0.6=6$$

$$a_3=a_1·r^{n-1}=10\cdot {0.6}^{3-1}=10\cdot {0.6}^2=10\cdot 0.36=3.5999999999999996$$

$$a_4=a_1·r^{n-1}=10\cdot {0.6}^{4-1}=10\cdot {0.6}^3=10\cdot 0.21599999999999997=2.1599999999999997$$

$$a_5=a_1·r^{n-1}=10\cdot {0.6}^{5-1}=10\cdot {0.6}^4=10\cdot 0.1296=1.2959999999999998$$

$$a_6=a_1·r^{n-1}=10\cdot {0.6}^{6-1}=10\cdot {0.6}^5=10\cdot 0.07775999999999998=0.7775999999999998$$

$$a_7=a_1·r^{n-1}=10\cdot {0.6}^{7-1}=10\cdot {0.6}^6=10\cdot 0.04665599999999999=0.46655999999999986$$

$$a_8=a_1·r^{n-1}=10\cdot {0.6}^{8-1}=10\cdot {0.6}^7=10\cdot 0.027993599999999993=0.27993599999999996$$

$$a_9=a_1·r^{n-1}=10\cdot {0.6}^{9-1}=10\cdot {0.6}^8=10\cdot 0.016796159999999994=0.16796159999999993$$

$$a_{10}=a_1·r^{n-1}=10\cdot {0.6}^{10-1}=10\cdot {0.6}^9=10\cdot 0.010077695999999997=0.10077695999999997$$