解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=20$$ 和公比：$$r=0.6$$ 插入几何级数的公式：

$$a_1=20$$

$$a_2=a_1·r^{n-1}=20\cdot {0.6}^{2-1}=20\cdot {0.6}^1=20\cdot 0.6=12$$

$$a_3=a_1·r^{n-1}=20\cdot {0.6}^{3-1}=20\cdot {0.6}^2=20\cdot 0.36=7.199999999999999$$

$$a_4=a_1·r^{n-1}=20\cdot {0.6}^{4-1}=20\cdot {0.6}^3=20\cdot 0.21599999999999997=4.319999999999999$$

$$a_5=a_1·r^{n-1}=20\cdot {0.6}^{5-1}=20\cdot {0.6}^4=20\cdot 0.1296=2.5919999999999996$$

$$a_6=a_1·r^{n-1}=20\cdot {0.6}^{6-1}=20\cdot {0.6}^5=20\cdot 0.07775999999999998=1.5551999999999997$$

$$a_7=a_1·r^{n-1}=20\cdot {0.6}^{7-1}=20\cdot {0.6}^6=20\cdot 0.04665599999999999=0.9331199999999997$$

$$a_8=a_1·r^{n-1}=20\cdot {0.6}^{8-1}=20\cdot {0.6}^7=20\cdot 0.027993599999999993=0.5598719999999999$$

$$a_9=a_1·r^{n-1}=20\cdot {0.6}^{9-1}=20\cdot {0.6}^8=20\cdot 0.016796159999999994=0.33592319999999987$$

$$a_{10}=a_1·r^{n-1}=20\cdot {0.6}^{10-1}=20\cdot {0.6}^9=20\cdot 0.010077695999999997=0.20155391999999994$$