解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=108$$ 和公比：$$r=0.75$$ 插入几何级数的公式：

$$a_1=108$$

$$a_2=a_1·r^{n-1}=108\cdot {0.75}^{2-1}=108\cdot {0.75}^1=108\cdot 0.75=81$$

$$a_3=a_1·r^{n-1}=108\cdot {0.75}^{3-1}=108\cdot {0.75}^2=108\cdot 0.5625=60.75$$

$$a_4=a_1·r^{n-1}=108\cdot {0.75}^{4-1}=108\cdot {0.75}^3=108\cdot 0.421875=45.5625$$

$$a_5=a_1·r^{n-1}=108\cdot {0.75}^{5-1}=108\cdot {0.75}^4=108\cdot 0.31640625=34.171875$$

$$a_6=a_1·r^{n-1}=108\cdot {0.75}^{6-1}=108\cdot {0.75}^5=108\cdot 0.2373046875=25.62890625$$

$$a_7=a_1·r^{n-1}=108\cdot {0.75}^{7-1}=108\cdot {0.75}^6=108\cdot 0.177978515625=19.2216796875$$

$$a_8=a_1·r^{n-1}=108\cdot {0.75}^{8-1}=108\cdot {0.75}^7=108\cdot 0.13348388671875=14.416259765625$$

$$a_9=a_1·r^{n-1}=108\cdot {0.75}^{9-1}=108\cdot {0.75}^8=108\cdot 0.1001129150390625=10.81219482421875$$

$$a_{10}=a_1·r^{n-1}=108\cdot {0.75}^{10-1}=108\cdot {0.75}^9=108\cdot 0.07508468627929688=8.109146118164062$$