解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=75$$ 和公比：$$r=2.2$$ 插入几何级数的公式：

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {2.2}^{2-1}=75\cdot {2.2}^1=75\cdot 2.2=165$$

$$a_3=a_1·r^{n-1}=75\cdot {2.2}^{3-1}=75\cdot {2.2}^2=75\cdot 4.840000000000001=363.00000000000006$$

$$a_4=a_1·r^{n-1}=75\cdot {2.2}^{4-1}=75\cdot {2.2}^3=75\cdot 10.648000000000003=798.6000000000003$$

$$a_5=a_1·r^{n-1}=75\cdot {2.2}^{5-1}=75\cdot {2.2}^4=75\cdot 23.425600000000006=1756.9200000000005$$

$$a_6=a_1·r^{n-1}=75\cdot {2.2}^{6-1}=75\cdot {2.2}^5=75\cdot 51.53632000000002=3865.2240000000015$$

$$a_7=a_1·r^{n-1}=75\cdot {2.2}^{7-1}=75\cdot {2.2}^6=75\cdot 113.37990400000005=8503.492800000004$$

$$a_8=a_1·r^{n-1}=75\cdot {2.2}^{8-1}=75\cdot {2.2}^7=75\cdot 249.43578880000015=18707.68416000001$$

$$a_9=a_1·r^{n-1}=75\cdot {2.2}^{9-1}=75\cdot {2.2}^8=75\cdot 548.7587353600004=41156.90515200003$$

$$a_{10}=a_1·r^{n-1}=75\cdot {2.2}^{10-1}=75\cdot {2.2}^9=75\cdot 1207.269217792001=90545.19133440008$$