解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=150$$ 和公比：$$r=0.56$$ 插入几何级数的公式：

$$a_1=150$$

$$a_2=a_1·r^{n-1}=150\cdot {0.56}^{2-1}=150\cdot {0.56}^1=150\cdot 0.56=84.00000000000001$$

$$a_3=a_1·r^{n-1}=150\cdot {0.56}^{3-1}=150\cdot {0.56}^2=150\cdot 0.31360000000000005=47.040000000000006$$

$$a_4=a_1·r^{n-1}=150\cdot {0.56}^{4-1}=150\cdot {0.56}^3=150\cdot 0.17561600000000005=26.34240000000001$$

$$a_5=a_1·r^{n-1}=150\cdot {0.56}^{5-1}=150\cdot {0.56}^4=150\cdot 0.09834496000000004=14.751744000000006$$

$$a_6=a_1·r^{n-1}=150\cdot {0.56}^{6-1}=150\cdot {0.56}^5=150\cdot 0.05507317760000002=8.260976640000003$$

$$a_7=a_1·r^{n-1}=150\cdot {0.56}^{7-1}=150\cdot {0.56}^6=150\cdot 0.030840979456000017=4.626146918400003$$

$$a_8=a_1·r^{n-1}=150\cdot {0.56}^{8-1}=150\cdot {0.56}^7=150\cdot 0.01727094849536001=2.5906422743040016$$

$$a_9=a_1·r^{n-1}=150\cdot {0.56}^{9-1}=150\cdot {0.56}^8=150\cdot 0.009671731157401607=1.450759673610241$$

$$a_{10}=a_1·r^{n-1}=150\cdot {0.56}^{10-1}=150\cdot {0.56}^9=150\cdot 0.005416169448144901=0.8124254172217351$$