解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=42$$ 和公比：$$r=2.2857142857142856$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{2-1}=42\cdot {2.2857142857142856}^1=42\cdot 2.2857142857142856=96$$

$$a_3=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{3-1}=42\cdot {2.2857142857142856}^2=42\cdot 5.224489795918367=219.42857142857142$$

$$a_4=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{4-1}=42\cdot {2.2857142857142856}^3=42\cdot 11.941690962099123=501.5510204081632$$

$$a_5=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{5-1}=42\cdot {2.2857142857142856}^4=42\cdot 27.295293627655138=1146.4023323615158$$

$$a_6=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{6-1}=42\cdot {2.2857142857142856}^5=42\cdot 62.389242577497455=2620.348188254893$$

$$a_7=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{7-1}=42\cdot {2.2857142857142856}^6=42\cdot 142.60398303427988=5989.367287439755$$

$$a_8=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{8-1}=42\cdot {2.2857142857142856}^7=42\cdot 325.95196122121115=13689.98237129087$$

$$a_9=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{9-1}=42\cdot {2.2857142857142856}^8=42\cdot 745.0330542199112=31291.388277236267$$

$$a_{10}=a_1·r^{n-1}=42\cdot {2.2857142857142856}^{10-1}=42\cdot {2.2857142857142856}^9=42\cdot 1702.9326953597968=71523.17320511147$$