解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=500$$ 和公比：$$r=1.34$$ 插入几何级数的公式：

$$a_1=500$$

$$a_2=a_1·r^{n-1}=500\cdot {1.34}^{2-1}=500\cdot {1.34}^1=500\cdot 1.34=670$$

$$a_3=a_1·r^{n-1}=500\cdot {1.34}^{3-1}=500\cdot {1.34}^2=500\cdot 1.7956000000000003=897.8000000000002$$

$$a_4=a_1·r^{n-1}=500\cdot {1.34}^{4-1}=500\cdot {1.34}^3=500\cdot 2.4061040000000005=1203.0520000000001$$

$$a_5=a_1·r^{n-1}=500\cdot {1.34}^{5-1}=500\cdot {1.34}^4=500\cdot 3.224179360000001=1612.0896800000005$$

$$a_6=a_1·r^{n-1}=500\cdot {1.34}^{6-1}=500\cdot {1.34}^5=500\cdot 4.320400342400001=2160.2001712000006$$

$$a_7=a_1·r^{n-1}=500\cdot {1.34}^{7-1}=500\cdot {1.34}^6=500\cdot 5.789336458816002=2894.668229408001$$

$$a_8=a_1·r^{n-1}=500\cdot {1.34}^{8-1}=500\cdot {1.34}^7=500\cdot 7.7577108548134435=3878.855427406722$$

$$a_9=a_1·r^{n-1}=500\cdot {1.34}^{9-1}=500\cdot {1.34}^8=500\cdot 10.395332545450014=5197.666272725007$$

$$a_{10}=a_1·r^{n-1}=500\cdot {1.34}^{10-1}=500\cdot {1.34}^9=500\cdot 13.929745610903021=6964.87280545151$$