解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=500$$ 和公比：$$r=0.56$$ 插入几何级数的公式：

$$a_1=500$$

$$a_2=a_1·r^{n-1}=500\cdot {0.56}^{2-1}=500\cdot {0.56}^1=500\cdot 0.56=280$$

$$a_3=a_1·r^{n-1}=500\cdot {0.56}^{3-1}=500\cdot {0.56}^2=500\cdot 0.31360000000000005=156.8$$

$$a_4=a_1·r^{n-1}=500\cdot {0.56}^{4-1}=500\cdot {0.56}^3=500\cdot 0.17561600000000005=87.80800000000002$$

$$a_5=a_1·r^{n-1}=500\cdot {0.56}^{5-1}=500\cdot {0.56}^4=500\cdot 0.09834496000000004=49.17248000000002$$

$$a_6=a_1·r^{n-1}=500\cdot {0.56}^{6-1}=500\cdot {0.56}^5=500\cdot 0.05507317760000002=27.53658880000001$$

$$a_7=a_1·r^{n-1}=500\cdot {0.56}^{7-1}=500\cdot {0.56}^6=500\cdot 0.030840979456000017=15.420489728000009$$

$$a_8=a_1·r^{n-1}=500\cdot {0.56}^{8-1}=500\cdot {0.56}^7=500\cdot 0.01727094849536001=8.635474247680005$$

$$a_9=a_1·r^{n-1}=500\cdot {0.56}^{9-1}=500\cdot {0.56}^8=500\cdot 0.009671731157401607=4.835865578700804$$

$$a_{10}=a_1·r^{n-1}=500\cdot {0.56}^{10-1}=500\cdot {0.56}^9=500\cdot 0.005416169448144901=2.7080847240724504$$