解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=140$$ 和公比：$$r=1.8$$ 插入几何级数的公式：

$$a_1=140$$

$$a_2=a_1·r^{n-1}=140\cdot {1.8}^{2-1}=140\cdot {1.8}^1=140\cdot 1.8=252$$

$$a_3=a_1·r^{n-1}=140\cdot {1.8}^{3-1}=140\cdot {1.8}^2=140\cdot 3.24=453.6$$

$$a_4=a_1·r^{n-1}=140\cdot {1.8}^{4-1}=140\cdot {1.8}^3=140\cdot 5.832000000000001=816.4800000000001$$

$$a_5=a_1·r^{n-1}=140\cdot {1.8}^{5-1}=140\cdot {1.8}^4=140\cdot 10.4976=1469.664$$

$$a_6=a_1·r^{n-1}=140\cdot {1.8}^{6-1}=140\cdot {1.8}^5=140\cdot 18.895680000000002=2645.3952000000004$$

$$a_7=a_1·r^{n-1}=140\cdot {1.8}^{7-1}=140\cdot {1.8}^6=140\cdot 34.012224=4761.71136$$

$$a_8=a_1·r^{n-1}=140\cdot {1.8}^{8-1}=140\cdot {1.8}^7=140\cdot 61.22200320000001=8571.080448$$

$$a_9=a_1·r^{n-1}=140\cdot {1.8}^{9-1}=140\cdot {1.8}^8=140\cdot 110.19960576000003=15427.944806400004$$

$$a_{10}=a_1·r^{n-1}=140\cdot {1.8}^{10-1}=140\cdot {1.8}^9=140\cdot 198.35929036800005=27770.300651520007$$