解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=20$$ 和公比：$$r=1.35$$ 插入几何级数的公式：

$$a_1=20$$

$$a_2=a_1·r^{n-1}=20\cdot {1.35}^{2-1}=20\cdot {1.35}^1=20\cdot 1.35=27$$

$$a_3=a_1·r^{n-1}=20\cdot {1.35}^{3-1}=20\cdot {1.35}^2=20\cdot 1.8225000000000002=36.45$$

$$a_4=a_1·r^{n-1}=20\cdot {1.35}^{4-1}=20\cdot {1.35}^3=20\cdot 2.4603750000000004=49.20750000000001$$

$$a_5=a_1·r^{n-1}=20\cdot {1.35}^{5-1}=20\cdot {1.35}^4=20\cdot 3.321506250000001=66.43012500000002$$

$$a_6=a_1·r^{n-1}=20\cdot {1.35}^{6-1}=20\cdot {1.35}^5=20\cdot 4.484033437500002=89.68066875000004$$

$$a_7=a_1·r^{n-1}=20\cdot {1.35}^{7-1}=20\cdot {1.35}^6=20\cdot 6.053445140625002=121.06890281250004$$

$$a_8=a_1·r^{n-1}=20\cdot {1.35}^{8-1}=20\cdot {1.35}^7=20\cdot 8.172150939843753=163.44301879687507$$

$$a_9=a_1·r^{n-1}=20\cdot {1.35}^{9-1}=20\cdot {1.35}^8=20\cdot 11.032403768789068=220.64807537578136$$

$$a_{10}=a_1·r^{n-1}=20\cdot {1.35}^{10-1}=20\cdot {1.35}^9=20\cdot 14.893745087865243=297.8749017573049$$