解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=860$$ 和公比：$$r=0.6$$ 插入几何级数的公式：

$$a_1=860$$

$$a_2=a_1·r^{n-1}=860\cdot {0.6}^{2-1}=860\cdot {0.6}^1=860\cdot 0.6=516$$

$$a_3=a_1·r^{n-1}=860\cdot {0.6}^{3-1}=860\cdot {0.6}^2=860\cdot 0.36=309.59999999999997$$

$$a_4=a_1·r^{n-1}=860\cdot {0.6}^{4-1}=860\cdot {0.6}^3=860\cdot 0.21599999999999997=185.75999999999996$$

$$a_5=a_1·r^{n-1}=860\cdot {0.6}^{5-1}=860\cdot {0.6}^4=860\cdot 0.1296=111.45599999999999$$

$$a_6=a_1·r^{n-1}=860\cdot {0.6}^{6-1}=860\cdot {0.6}^5=860\cdot 0.07775999999999998=66.87359999999998$$

$$a_7=a_1·r^{n-1}=860\cdot {0.6}^{7-1}=860\cdot {0.6}^6=860\cdot 0.04665599999999999=40.12415999999999$$

$$a_8=a_1·r^{n-1}=860\cdot {0.6}^{8-1}=860\cdot {0.6}^7=860\cdot 0.027993599999999993=24.074495999999993$$

$$a_9=a_1·r^{n-1}=860\cdot {0.6}^{9-1}=860\cdot {0.6}^8=860\cdot 0.016796159999999994=14.444697599999994$$

$$a_{10}=a_1·r^{n-1}=860\cdot {0.6}^{10-1}=860\cdot {0.6}^9=860\cdot 0.010077695999999997=8.666818559999998$$