解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=546$$ 和公比：$$r=3.6538461538461537$$ 插入几何级数的公式：

$$a_1=546$$

$$a_2=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{2-1}=546\cdot {3.6538461538461537}^1=546\cdot 3.6538461538461537=1995$$

$$a_3=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{3-1}=546\cdot {3.6538461538461537}^2=546\cdot 13.35059171597633=7289.423076923076$$

$$a_4=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{4-1}=546\cdot {3.6538461538461537}^3=546\cdot 48.781008192990434=26634.430473372777$$

$$a_5=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{5-1}=546\cdot {3.6538461538461537}^4=546\cdot 178.2382991666958=97318.11134501592$$

$$a_6=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{6-1}=546\cdot {3.6538461538461537}^5=546\cdot 651.2553238783116=355585.40683755814$$

$$a_7=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{7-1}=546\cdot {3.6538461538461537}^6=546\cdot 2379.5867603246=1299254.3711372316$$

$$a_8=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{8-1}=546\cdot {3.6538461538461537}^7=546\cdot 8694.64393195527=4747275.586847577$$

$$a_9=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{9-1}=546\cdot {3.6538461538461537}^8=546\cdot 31768.89128983656=17345814.64425076$$

$$a_{10}=a_1·r^{n-1}=546\cdot {3.6538461538461537}^{10-1}=546\cdot {3.6538461538461537}^9=546\cdot 116078.6412513259=63378938.12322394$$