解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=2,500$$ 和公比：$$r=0.56$$ 插入几何级数的公式：

$$a_1=2500$$

$$a_2=a_1·r^{n-1}=2500\cdot {0.56}^{2-1}=2500\cdot {0.56}^1=2500\cdot 0.56=1400.0000000000002$$

$$a_3=a_1·r^{n-1}=2500\cdot {0.56}^{3-1}=2500\cdot {0.56}^2=2500\cdot 0.31360000000000005=784.0000000000001$$

$$a_4=a_1·r^{n-1}=2500\cdot {0.56}^{4-1}=2500\cdot {0.56}^3=2500\cdot 0.17561600000000005=439.04000000000013$$

$$a_5=a_1·r^{n-1}=2500\cdot {0.56}^{5-1}=2500\cdot {0.56}^4=2500\cdot 0.09834496000000004=245.8624000000001$$

$$a_6=a_1·r^{n-1}=2500\cdot {0.56}^{6-1}=2500\cdot {0.56}^5=2500\cdot 0.05507317760000002=137.68294400000005$$

$$a_7=a_1·r^{n-1}=2500\cdot {0.56}^{7-1}=2500\cdot {0.56}^6=2500\cdot 0.030840979456000017=77.10244864000005$$

$$a_8=a_1·r^{n-1}=2500\cdot {0.56}^{8-1}=2500\cdot {0.56}^7=2500\cdot 0.01727094849536001=43.17737123840003$$

$$a_9=a_1·r^{n-1}=2500\cdot {0.56}^{9-1}=2500\cdot {0.56}^8=2500\cdot 0.009671731157401607=24.179327893504016$$

$$a_{10}=a_1·r^{n-1}=2500\cdot {0.56}^{10-1}=2500\cdot {0.56}^9=2500\cdot 0.005416169448144901=13.540423620362251$$