解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=55$$ 和公比：$$r=1.8181818181818181$$ 插入几何级数的公式：

$$a_1=55$$

$$a_2=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{2-1}=55\cdot {1.8181818181818181}^1=55\cdot 1.8181818181818181=100$$

$$a_3=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{3-1}=55\cdot {1.8181818181818181}^2=55\cdot 3.305785123966942=181.8181818181818$$

$$a_4=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{4-1}=55\cdot {1.8181818181818181}^3=55\cdot 6.010518407212621=330.5785123966942$$

$$a_5=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{5-1}=55\cdot {1.8181818181818181}^4=55\cdot 10.92821528584113=601.0518407212621$$

$$a_6=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{6-1}=55\cdot {1.8181818181818181}^5=55\cdot 19.86948233789296=1092.821528584113$$

$$a_7=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{7-1}=55\cdot {1.8181818181818181}^6=55\cdot 36.12633152344175=1986.9482337892962$$

$$a_8=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{8-1}=55\cdot {1.8181818181818181}^7=55\cdot 65.68423913353045=3612.633152344175$$

$$a_9=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{9-1}=55\cdot {1.8181818181818181}^8=55\cdot 119.42588933369173=6568.4239133530455$$

$$a_{10}=a_1·r^{n-1}=55\cdot {1.8181818181818181}^{10-1}=55\cdot {1.8181818181818181}^9=55\cdot 217.1379806067122=11942.588933369172$$