解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=14,112$$ 和公比：$$r=0.6428571428571429$$ 插入几何级数的公式：

$$a_1=14112$$

$$a_2=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{2-1}=14112\cdot {0.6428571428571429}^1=14112\cdot 0.6428571428571429=9072$$

$$a_3=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{3-1}=14112\cdot {0.6428571428571429}^2=14112\cdot 0.41326530612244905=5832.000000000001$$

$$a_4=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{4-1}=14112\cdot {0.6428571428571429}^3=14112\cdot 0.26567055393586014=3749.1428571428582$$

$$a_5=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{5-1}=14112\cdot {0.6428571428571429}^4=14112\cdot 0.1707882132444815=2410.1632653061233$$

$$a_6=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{6-1}=14112\cdot {0.6428571428571429}^5=14112\cdot 0.10979242280002384=1549.3906705539364$$

$$a_7=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{7-1}=14112\cdot {0.6428571428571429}^6=14112\cdot 0.07058084322858676=996.0368596418165$$

$$a_8=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{8-1}=14112\cdot {0.6428571428571429}^7=14112\cdot 0.04537339921837721=640.3094097697391$$

$$a_9=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{9-1}=14112\cdot {0.6428571428571429}^8=14112\cdot 0.02916861378324249=411.627477709118$$

$$a_{10}=a_1·r^{n-1}=14112\cdot {0.6428571428571429}^{10-1}=14112\cdot {0.6428571428571429}^9=14112\cdot 0.018751251717798748=264.61766424157594$$