解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=32$$ 和公比：$$r=1.375$$ 插入几何级数的公式：

$$a_1=32$$

$$a_2=a_1·r^{n-1}=32\cdot {1.375}^{2-1}=32\cdot {1.375}^1=32\cdot 1.375=44$$

$$a_3=a_1·r^{n-1}=32\cdot {1.375}^{3-1}=32\cdot {1.375}^2=32\cdot 1.890625=60.5$$

$$a_4=a_1·r^{n-1}=32\cdot {1.375}^{4-1}=32\cdot {1.375}^3=32\cdot 2.599609375=83.1875$$

$$a_5=a_1·r^{n-1}=32\cdot {1.375}^{5-1}=32\cdot {1.375}^4=32\cdot 3.574462890625=114.3828125$$

$$a_6=a_1·r^{n-1}=32\cdot {1.375}^{6-1}=32\cdot {1.375}^5=32\cdot 4.914886474609375=157.2763671875$$

$$a_7=a_1·r^{n-1}=32\cdot {1.375}^{7-1}=32\cdot {1.375}^6=32\cdot 6.757968902587891=216.2550048828125$$

$$a_8=a_1·r^{n-1}=32\cdot {1.375}^{8-1}=32\cdot {1.375}^7=32\cdot 9.29220724105835=297.3506317138672$$

$$a_9=a_1·r^{n-1}=32\cdot {1.375}^{9-1}=32\cdot {1.375}^8=32\cdot 12.77678495645523=408.8571186065674$$

$$a_{10}=a_1·r^{n-1}=32\cdot {1.375}^{10-1}=32\cdot {1.375}^9=32\cdot 17.568079315125942=562.1785380840302$$