解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=60$$ 和公比：$$r=1.55$$ 插入几何级数的公式：

$$a_1=60$$

$$a_2=a_1·r^{n-1}=60\cdot {1.55}^{2-1}=60\cdot {1.55}^1=60\cdot 1.55=93$$

$$a_3=a_1·r^{n-1}=60\cdot {1.55}^{3-1}=60\cdot {1.55}^2=60\cdot 2.4025000000000003=144.15$$

$$a_4=a_1·r^{n-1}=60\cdot {1.55}^{4-1}=60\cdot {1.55}^3=60\cdot 3.7238750000000005=223.43250000000003$$

$$a_5=a_1·r^{n-1}=60\cdot {1.55}^{5-1}=60\cdot {1.55}^4=60\cdot 5.7720062500000004=346.320375$$

$$a_6=a_1·r^{n-1}=60\cdot {1.55}^{6-1}=60\cdot {1.55}^5=60\cdot 8.9466096875=536.79658125$$

$$a_7=a_1·r^{n-1}=60\cdot {1.55}^{7-1}=60\cdot {1.55}^6=60\cdot 13.867245015625002=832.0347009375001$$

$$a_8=a_1·r^{n-1}=60\cdot {1.55}^{8-1}=60\cdot {1.55}^7=60\cdot 21.494229774218756=1289.6537864531253$$

$$a_9=a_1·r^{n-1}=60\cdot {1.55}^{9-1}=60\cdot {1.55}^8=60\cdot 33.31605615003907=1998.963369002344$$

$$a_{10}=a_1·r^{n-1}=60\cdot {1.55}^{10-1}=60\cdot {1.55}^9=60\cdot 51.63988703256056=3098.3932219536337$$