解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=65$$ 和公比：$$r=6.153846153846154$$ 插入几何级数的公式：

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {6.153846153846154}^{2-1}=65\cdot {6.153846153846154}^1=65\cdot 6.153846153846154=400$$

$$a_3=a_1·r^{n-1}=65\cdot {6.153846153846154}^{3-1}=65\cdot {6.153846153846154}^2=65\cdot 37.8698224852071=2461.5384615384614$$

$$a_4=a_1·r^{n-1}=65\cdot {6.153846153846154}^{4-1}=65\cdot {6.153846153846154}^3=65\cdot 233.04506144742834=15147.928994082842$$

$$a_5=a_1·r^{n-1}=65\cdot {6.153846153846154}^{5-1}=65\cdot {6.153846153846154}^4=65\cdot 1434.1234550610977=93218.02457897135$$

$$a_6=a_1·r^{n-1}=65\cdot {6.153846153846154}^{6-1}=65\cdot {6.153846153846154}^5=65\cdot 8825.375108068294=573649.3820244392$$

$$a_7=a_1·r^{n-1}=65\cdot {6.153846153846154}^{7-1}=65\cdot {6.153846153846154}^6=65\cdot 54310.00066503566=3530150.0432273177$$

$$a_8=a_1·r^{n-1}=65\cdot {6.153846153846154}^{8-1}=65\cdot {6.153846153846154}^7=65\cdot 334215.38870791177=21724000.266014267$$

$$a_9=a_1·r^{n-1}=65\cdot {6.153846153846154}^{9-1}=65\cdot {6.153846153846154}^8=65\cdot 2056710.0843563802=133686155.48316471$$

$$a_{10}=a_1·r^{n-1}=65\cdot {6.153846153846154}^{10-1}=65\cdot {6.153846153846154}^9=65\cdot 12656677.44219311=822684033.7425522$$