解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=280$$ 和公比：$$r=4.446428571428571$$ 插入几何级数的公式：

$$a_1=280$$

$$a_2=a_1·r^{n-1}=280\cdot {4.446428571428571}^{2-1}=280\cdot {4.446428571428571}^1=280\cdot 4.446428571428571=1245$$

$$a_3=a_1·r^{n-1}=280\cdot {4.446428571428571}^{3-1}=280\cdot {4.446428571428571}^2=280\cdot 19.770727040816325=5535.803571428571$$

$$a_4=a_1·r^{n-1}=280\cdot {4.446428571428571}^{4-1}=280\cdot {4.446428571428571}^3=280\cdot 87.90912559220115=24614.55516581632$$

$$a_5=a_1·r^{n-1}=280\cdot {4.446428571428571}^{5-1}=280\cdot {4.446428571428571}^4=280\cdot 390.8816477224658=109446.86136229042$$

$$a_6=a_1·r^{n-1}=280\cdot {4.446428571428571}^{6-1}=280\cdot {4.446428571428571}^5=280\cdot 1738.0273264802497=486647.65141446993$$

$$a_7=a_1·r^{n-1}=280\cdot {4.446428571428571}^{7-1}=280\cdot {4.446428571428571}^6=280\cdot 7728.0143623853955=2163844.0214679106$$

$$a_8=a_1·r^{n-1}=280\cdot {4.446428571428571}^{8-1}=280\cdot {4.446428571428571}^7=280\cdot 34362.06386132078=9621377.881169818$$

$$a_9=a_1·r^{n-1}=280\cdot {4.446428571428571}^{9-1}=280\cdot {4.446428571428571}^8=280\cdot 152788.46252622985=42780769.50734436$$

$$a_{10}=a_1·r^{n-1}=280\cdot {4.446428571428571}^{10-1}=280\cdot {4.446428571428571}^9=280\cdot 679362.985161272=190221635.84515616$$