解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=40$$ 和公比：$$r=1.6$$ 插入几何级数的公式：

$$a_1=40$$

$$a_2=a_1·r^{n-1}=40\cdot {1.6}^{2-1}=40\cdot {1.6}^1=40\cdot 1.6=64$$

$$a_3=a_1·r^{n-1}=40\cdot {1.6}^{3-1}=40\cdot {1.6}^2=40\cdot 2.5600000000000005=102.40000000000002$$

$$a_4=a_1·r^{n-1}=40\cdot {1.6}^{4-1}=40\cdot {1.6}^3=40\cdot 4.096000000000001=163.84000000000003$$

$$a_5=a_1·r^{n-1}=40\cdot {1.6}^{5-1}=40\cdot {1.6}^4=40\cdot 6.553600000000001=262.14400000000006$$

$$a_6=a_1·r^{n-1}=40\cdot {1.6}^{6-1}=40\cdot {1.6}^5=40\cdot 10.485760000000003=419.4304000000001$$

$$a_7=a_1·r^{n-1}=40\cdot {1.6}^{7-1}=40\cdot {1.6}^6=40\cdot 16.777216000000006=671.0886400000003$$

$$a_8=a_1·r^{n-1}=40\cdot {1.6}^{8-1}=40\cdot {1.6}^7=40\cdot 26.84354560000001=1073.7418240000004$$

$$a_9=a_1·r^{n-1}=40\cdot {1.6}^{9-1}=40\cdot {1.6}^8=40\cdot 42.94967296000002=1717.9869184000008$$

$$a_{10}=a_1·r^{n-1}=40\cdot {1.6}^{10-1}=40\cdot {1.6}^9=40\cdot 68.71947673600003=2748.7790694400014$$