解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=124$$ 和公比：$$r=0.75$$ 插入几何级数的公式：

$$a_1=124$$

$$a_2=a_1·r^{n-1}=124\cdot {0.75}^{2-1}=124\cdot {0.75}^1=124\cdot 0.75=93$$

$$a_3=a_1·r^{n-1}=124\cdot {0.75}^{3-1}=124\cdot {0.75}^2=124\cdot 0.5625=69.75$$

$$a_4=a_1·r^{n-1}=124\cdot {0.75}^{4-1}=124\cdot {0.75}^3=124\cdot 0.421875=52.3125$$

$$a_5=a_1·r^{n-1}=124\cdot {0.75}^{5-1}=124\cdot {0.75}^4=124\cdot 0.31640625=39.234375$$

$$a_6=a_1·r^{n-1}=124\cdot {0.75}^{6-1}=124\cdot {0.75}^5=124\cdot 0.2373046875=29.42578125$$

$$a_7=a_1·r^{n-1}=124\cdot {0.75}^{7-1}=124\cdot {0.75}^6=124\cdot 0.177978515625=22.0693359375$$

$$a_8=a_1·r^{n-1}=124\cdot {0.75}^{8-1}=124\cdot {0.75}^7=124\cdot 0.13348388671875=16.552001953125$$

$$a_9=a_1·r^{n-1}=124\cdot {0.75}^{9-1}=124\cdot {0.75}^8=124\cdot 0.1001129150390625=12.41400146484375$$

$$a_{10}=a_1·r^{n-1}=124\cdot {0.75}^{10-1}=124\cdot {0.75}^9=124\cdot 0.07508468627929688=9.310501098632812$$