解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=147$$ 和公比：$$r=1.3061224489795917$$ 插入几何级数的公式：

$$a_1=147$$

$$a_2=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{2-1}=147\cdot {1.3061224489795917}^1=147\cdot 1.3061224489795917=191.99999999999997$$

$$a_3=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{3-1}=147\cdot {1.3061224489795917}^2=147\cdot 1.705955851728446=250.77551020408157$$

$$a_4=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{4-1}=147\cdot {1.3061224489795917}^3=147\cdot 2.2281872349106235=327.54352353186164$$

$$a_5=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{5-1}=147\cdot {1.3061224489795917}^4=147\cdot 2.9102853680465284=427.81194910283966$$

$$a_6=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{6-1}=147\cdot {1.3061224489795917}^5=147\cdot 3.801189052142404=558.7747906649334$$

$$a_7=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{7-1}=147\cdot {1.3061224489795917}^6=147\cdot 4.96481835381865=729.8282980113415$$

$$a_8=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{8-1}=147\cdot {1.3061224489795917}^7=147\cdot 6.48466070702844=953.2451239331807$$

$$a_9=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{9-1}=147\cdot {1.3061224489795917}^8=147\cdot 8.469760923465717=1245.0548557494603$$

$$a_{10}=a_1·r^{n-1}=147\cdot {1.3061224489795917}^{10-1}=147\cdot {1.3061224489795917}^9=147\cdot 11.06254487962869=1626.1940973054175$$