解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=5$$ 和公比：$$r=4.6$$ 插入几何级数的公式：

$$a_1=5$$

$$a_2=a_1·r^{n-1}=5\cdot {4.6}^{2-1}=5\cdot {4.6}^1=5\cdot 4.6=23$$

$$a_3=a_1·r^{n-1}=5\cdot {4.6}^{3-1}=5\cdot {4.6}^2=5\cdot 21.159999999999997=105.79999999999998$$

$$a_4=a_1·r^{n-1}=5\cdot {4.6}^{4-1}=5\cdot {4.6}^3=5\cdot 97.33599999999998=486.67999999999995$$

$$a_5=a_1·r^{n-1}=5\cdot {4.6}^{5-1}=5\cdot {4.6}^4=5\cdot 447.74559999999985=2238.727999999999$$

$$a_6=a_1·r^{n-1}=5\cdot {4.6}^{6-1}=5\cdot {4.6}^5=5\cdot 2059.6297599999994=10298.148799999997$$

$$a_7=a_1·r^{n-1}=5\cdot {4.6}^{7-1}=5\cdot {4.6}^6=5\cdot 9474.296895999996=47371.484479999985$$

$$a_8=a_1·r^{n-1}=5\cdot {4.6}^{8-1}=5\cdot {4.6}^7=5\cdot 43581.76572159998=217908.8286079999$$

$$a_9=a_1·r^{n-1}=5\cdot {4.6}^{9-1}=5\cdot {4.6}^8=5\cdot 200476.12231935989=1002380.6115967995$$

$$a_{10}=a_1·r^{n-1}=5\cdot {4.6}^{10-1}=5\cdot {4.6}^9=5\cdot 922190.1626690554=4610950.813345277$$