解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=105$$ 和公比：$$r=1.1904761904761905$$ 插入几何级数的公式：

$$a_1=105$$

$$a_2=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{2-1}=105\cdot {1.1904761904761905}^1=105\cdot 1.1904761904761905=125$$

$$a_3=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{3-1}=105\cdot {1.1904761904761905}^2=105\cdot 1.417233560090703=148.8095238095238$$

$$a_4=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{4-1}=105\cdot {1.1904761904761905}^3=105\cdot 1.6871828096317891=177.15419501133786$$

$$a_5=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{5-1}=105\cdot {1.1904761904761905}^4=105\cdot 2.008550963847368=210.89785120397366$$

$$a_6=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{6-1}=105\cdot {1.1904761904761905}^5=105\cdot 2.391132099818295=251.068870480921$$

$$a_7=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{7-1}=105\cdot {1.1904761904761905}^6=105\cdot 2.846585833117018=298.89151247728694$$

$$a_8=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{8-1}=105\cdot {1.1904761904761905}^7=105\cdot 3.3887926584726404=355.82322913962724$$

$$a_9=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{9-1}=105\cdot {1.1904761904761905}^8=105\cdot 4.034276974372191=423.5990823090801$$

$$a_{10}=a_1·r^{n-1}=105\cdot {1.1904761904761905}^{10-1}=105\cdot {1.1904761904761905}^9=105\cdot 4.802710683776418=504.2846217965239$$