解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=158$$ 和公比：$$r=1.2658227848101267$$ 插入几何级数的公式：

$$a_1=158$$

$$a_2=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{2-1}=158\cdot {1.2658227848101267}^1=158\cdot 1.2658227848101267=200$$

$$a_3=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{3-1}=158\cdot {1.2658227848101267}^2=158\cdot 1.6023073225444642=253.16455696202533$$

$$a_4=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{4-1}=158\cdot {1.2658227848101267}^3=158\cdot 2.0282371171448914=320.46146450889285$$

$$a_5=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{5-1}=158\cdot {1.2658227848101267}^4=158\cdot 2.56738875587961=405.64742342897836$$

$$a_6=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{6-1}=158\cdot {1.2658227848101267}^5=158\cdot 3.2498591846577343=513.477751175922$$

$$a_7=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{7-1}=158\cdot {1.2658227848101267}^6=158\cdot 4.11374580336422=649.9718369315468$$

$$a_8=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{8-1}=158\cdot {1.2658227848101267}^7=158\cdot 5.20727316881547=822.7491606728443$$

$$a_9=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{9-1}=158\cdot {1.2658227848101267}^8=158\cdot 6.59148502381705=1041.4546337630939$$

$$a_{10}=a_1·r^{n-1}=158\cdot {1.2658227848101267}^{10-1}=158\cdot {1.2658227848101267}^9=158\cdot 8.343651928882343=1318.29700476341$$