解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=256$$ 和公比：$$r=2.734375$$ 插入几何级数的公式：

$$a_1=256$$

$$a_2=a_1·r^{n-1}=256\cdot {2.734375}^{2-1}=256\cdot {2.734375}^1=256\cdot 2.734375=700$$

$$a_3=a_1·r^{n-1}=256\cdot {2.734375}^{3-1}=256\cdot {2.734375}^2=256\cdot 7.476806640625=1914.0625$$

$$a_4=a_1·r^{n-1}=256\cdot {2.734375}^{4-1}=256\cdot {2.734375}^3=256\cdot 20.444393157958984=5233.7646484375$$

$$a_5=a_1·r^{n-1}=256\cdot {2.734375}^{5-1}=256\cdot {2.734375}^4=256\cdot 55.9026375412941=14311.075210571289$$

$$a_6=a_1·r^{n-1}=256\cdot {2.734375}^{6-1}=256\cdot {2.734375}^5=256\cdot 152.85877452697605=39131.84627890587$$

$$a_7=a_1·r^{n-1}=256\cdot {2.734375}^{7-1}=256\cdot {2.734375}^6=256\cdot 417.97321159720013=107001.14216888323$$

$$a_8=a_1·r^{n-1}=256\cdot {2.734375}^{8-1}=256\cdot {2.734375}^7=256\cdot 1142.8955004610941=292581.2481180401$$

$$a_9=a_1·r^{n-1}=256\cdot {2.734375}^{9-1}=256\cdot {2.734375}^8=256\cdot 3125.104884073304=800026.8503227659$$

$$a_{10}=a_1·r^{n-1}=256\cdot {2.734375}^{10-1}=256\cdot {2.734375}^9=256\cdot 8545.208667387942=2187573.418851313$$