解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=42$$ 和公比：$$r=1.5714285714285714$$ 插入几何级数的公式：

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{2-1}=42\cdot {1.5714285714285714}^1=42\cdot 1.5714285714285714=66$$

$$a_3=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{3-1}=42\cdot {1.5714285714285714}^2=42\cdot 2.4693877551020407=103.71428571428571$$

$$a_4=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{4-1}=42\cdot {1.5714285714285714}^3=42\cdot 3.880466472303207=162.9795918367347$$

$$a_5=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{5-1}=42\cdot {1.5714285714285714}^4=42\cdot 6.0978758850478965=256.11078717201167$$

$$a_6=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{6-1}=42\cdot {1.5714285714285714}^5=42\cdot 9.582376390789552=402.45980841316117$$

$$a_7=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{7-1}=42\cdot {1.5714285714285714}^6=42\cdot 15.058020042669295=632.4368417921104$$

$$a_8=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{8-1}=42\cdot {1.5714285714285714}^7=42\cdot 23.662602924194605=993.8293228161734$$

$$a_9=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{9-1}=42\cdot {1.5714285714285714}^8=42\cdot 37.18409030944866=1561.731792996844$$

$$a_{10}=a_1·r^{n-1}=42\cdot {1.5714285714285714}^{10-1}=42\cdot {1.5714285714285714}^9=42\cdot 58.4321419148479=2454.1499604236114$$