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：$$r=0.6904761904761905$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{2-1}=42\cdot {0.6904761904761905}^1=42\cdot 0.6904761904761905=29$$

$$a_3=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{3-1}=42\cdot {0.6904761904761905}^2=42\cdot 0.4767573696145125=20.023809523809526$$

$$a_4=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{4-1}=42\cdot {0.6904761904761905}^3=42\cdot 0.32918961235287764=13.82596371882086$$

$$a_5=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{5-1}=42\cdot {0.6904761904761905}^4=42\cdot 0.22729758948174886=9.546498758233453$$

$$a_6=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{6-1}=42\cdot {0.6904761904761905}^5=42\cdot 0.15694357368977896=6.591630094970716$$

$$a_7=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{7-1}=42\cdot {0.6904761904761905}^6=42\cdot 0.10836580088103785=4.55136363700359$$

$$a_8=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{8-1}=42\cdot {0.6904761904761905}^7=42\cdot 0.07482400537024042=3.142608225550098$$

$$a_9=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{9-1}=42\cdot {0.6904761904761905}^8=42\cdot 0.05166419418421362=2.1698961557369723$$

$$a_{10}=a_1·r^{n-1}=42\cdot {0.6904761904761905}^{10-1}=42\cdot {0.6904761904761905}^9=42\cdot 0.035672895984337975=1.498261631342195$$