解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=70$$ 和公比：$$r=4.6$$ 插入几何级数的公式：

$$a_1=70$$

$$a_2=a_1·r^{n-1}=70\cdot {4.6}^{2-1}=70\cdot {4.6}^1=70\cdot 4.6=322$$

$$a_3=a_1·r^{n-1}=70\cdot {4.6}^{3-1}=70\cdot {4.6}^2=70\cdot 21.159999999999997=1481.1999999999998$$

$$a_4=a_1·r^{n-1}=70\cdot {4.6}^{4-1}=70\cdot {4.6}^3=70\cdot 97.33599999999998=6813.519999999999$$

$$a_5=a_1·r^{n-1}=70\cdot {4.6}^{5-1}=70\cdot {4.6}^4=70\cdot 447.74559999999985=31342.19199999999$$

$$a_6=a_1·r^{n-1}=70\cdot {4.6}^{6-1}=70\cdot {4.6}^5=70\cdot 2059.6297599999994=144174.08319999996$$

$$a_7=a_1·r^{n-1}=70\cdot {4.6}^{7-1}=70\cdot {4.6}^6=70\cdot 9474.296895999996=663200.7827199998$$

$$a_8=a_1·r^{n-1}=70\cdot {4.6}^{8-1}=70\cdot {4.6}^7=70\cdot 43581.76572159998=3050723.6005119984$$

$$a_9=a_1·r^{n-1}=70\cdot {4.6}^{9-1}=70\cdot {4.6}^8=70\cdot 200476.12231935989=14033328.562355192$$

$$a_{10}=a_1·r^{n-1}=70\cdot {4.6}^{10-1}=70\cdot {4.6}^9=70\cdot 922190.1626690554=64553311.38683388$$