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：$$r=1.3$$ 插入几何级数的公式：

$$a_1=20$$

$$a_2=a_1·r^{n-1}=20\cdot {1.3}^{2-1}=20\cdot {1.3}^1=20\cdot 1.3=26$$

$$a_3=a_1·r^{n-1}=20\cdot {1.3}^{3-1}=20\cdot {1.3}^2=20\cdot 1.6900000000000002=33.800000000000004$$

$$a_4=a_1·r^{n-1}=20\cdot {1.3}^{4-1}=20\cdot {1.3}^3=20\cdot 2.197=43.94$$

$$a_5=a_1·r^{n-1}=20\cdot {1.3}^{5-1}=20\cdot {1.3}^4=20\cdot 2.8561000000000005=57.122000000000014$$

$$a_6=a_1·r^{n-1}=20\cdot {1.3}^{6-1}=20\cdot {1.3}^5=20\cdot 3.7129300000000005=74.25860000000002$$

$$a_7=a_1·r^{n-1}=20\cdot {1.3}^{7-1}=20\cdot {1.3}^6=20\cdot 4.826809000000001=96.53618000000002$$

$$a_8=a_1·r^{n-1}=20\cdot {1.3}^{8-1}=20\cdot {1.3}^7=20\cdot 6.274851700000002=125.49703400000004$$

$$a_9=a_1·r^{n-1}=20\cdot {1.3}^{9-1}=20\cdot {1.3}^8=20\cdot 8.157307210000003=163.14614420000004$$

$$a_{10}=a_1·r^{n-1}=20\cdot {1.3}^{10-1}=20\cdot {1.3}^9=20\cdot 10.604499373000003=212.08998746000006$$