解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=144$$ 和公比：$$r=1.5625$$ 插入几何级数的公式：

$$a_1=144$$

$$a_2=a_1·r^{n-1}=144\cdot {1.5625}^{2-1}=144\cdot {1.5625}^1=144\cdot 1.5625=225$$

$$a_3=a_1·r^{n-1}=144\cdot {1.5625}^{3-1}=144\cdot {1.5625}^2=144\cdot 2.44140625=351.5625$$

$$a_4=a_1·r^{n-1}=144\cdot {1.5625}^{4-1}=144\cdot {1.5625}^3=144\cdot 3.814697265625=549.31640625$$

$$a_5=a_1·r^{n-1}=144\cdot {1.5625}^{5-1}=144\cdot {1.5625}^4=144\cdot 5.9604644775390625=858.306884765625$$

$$a_6=a_1·r^{n-1}=144\cdot {1.5625}^{6-1}=144\cdot {1.5625}^5=144\cdot 9.313225746154785=1341.104507446289$$

$$a_7=a_1·r^{n-1}=144\cdot {1.5625}^{7-1}=144\cdot {1.5625}^6=144\cdot 14.551915228366852=2095.4757928848267$$

$$a_8=a_1·r^{n-1}=144\cdot {1.5625}^{8-1}=144\cdot {1.5625}^7=144\cdot 22.737367544323206=3274.1809263825417$$

$$a_9=a_1·r^{n-1}=144\cdot {1.5625}^{9-1}=144\cdot {1.5625}^8=144\cdot 35.52713678800501=5115.907697472721$$

$$a_{10}=a_1·r^{n-1}=144\cdot {1.5625}^{10-1}=144\cdot {1.5625}^9=144\cdot 55.51115123125783=7993.605777301127$$