解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=200$$ 和公比：$$r=0.6$$ 插入几何级数的公式：

$$a_1=200$$

$$a_2=a_1·r^{n-1}=200\cdot {0.6}^{2-1}=200\cdot {0.6}^1=200\cdot 0.6=120$$

$$a_3=a_1·r^{n-1}=200\cdot {0.6}^{3-1}=200\cdot {0.6}^2=200\cdot 0.36=72$$

$$a_4=a_1·r^{n-1}=200\cdot {0.6}^{4-1}=200\cdot {0.6}^3=200\cdot 0.21599999999999997=43.199999999999996$$

$$a_5=a_1·r^{n-1}=200\cdot {0.6}^{5-1}=200\cdot {0.6}^4=200\cdot 0.1296=25.919999999999998$$

$$a_6=a_1·r^{n-1}=200\cdot {0.6}^{6-1}=200\cdot {0.6}^5=200\cdot 0.07775999999999998=15.551999999999996$$

$$a_7=a_1·r^{n-1}=200\cdot {0.6}^{7-1}=200\cdot {0.6}^6=200\cdot 0.04665599999999999=9.331199999999997$$

$$a_8=a_1·r^{n-1}=200\cdot {0.6}^{8-1}=200\cdot {0.6}^7=200\cdot 0.027993599999999993=5.598719999999998$$

$$a_9=a_1·r^{n-1}=200\cdot {0.6}^{9-1}=200\cdot {0.6}^8=200\cdot 0.016796159999999994=3.3592319999999987$$

$$a_{10}=a_1·r^{n-1}=200\cdot {0.6}^{10-1}=200\cdot {0.6}^9=200\cdot 0.010077695999999997=2.015539199999999$$