解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=55$$ 和公比：$$r=2.2$$ 插入几何级数的公式：

$$a_1=55$$

$$a_2=a_1·r^{n-1}=55\cdot {2.2}^{2-1}=55\cdot {2.2}^1=55\cdot 2.2=121.00000000000001$$

$$a_3=a_1·r^{n-1}=55\cdot {2.2}^{3-1}=55\cdot {2.2}^2=55\cdot 4.840000000000001=266.20000000000005$$

$$a_4=a_1·r^{n-1}=55\cdot {2.2}^{4-1}=55\cdot {2.2}^3=55\cdot 10.648000000000003=585.6400000000002$$

$$a_5=a_1·r^{n-1}=55\cdot {2.2}^{5-1}=55\cdot {2.2}^4=55\cdot 23.425600000000006=1288.4080000000004$$

$$a_6=a_1·r^{n-1}=55\cdot {2.2}^{6-1}=55\cdot {2.2}^5=55\cdot 51.53632000000002=2834.497600000001$$

$$a_7=a_1·r^{n-1}=55\cdot {2.2}^{7-1}=55\cdot {2.2}^6=55\cdot 113.37990400000005=6235.894720000003$$

$$a_8=a_1·r^{n-1}=55\cdot {2.2}^{8-1}=55\cdot {2.2}^7=55\cdot 249.43578880000015=13718.968384000009$$

$$a_9=a_1·r^{n-1}=55\cdot {2.2}^{9-1}=55\cdot {2.2}^8=55\cdot 548.7587353600004=30181.73044480002$$

$$a_{10}=a_1·r^{n-1}=55\cdot {2.2}^{10-1}=55\cdot {2.2}^9=55\cdot 1207.269217792001=66399.80697856005$$