解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=15$$ 和公比：$$r=4.2$$ 插入几何级数的公式：

$$a_1=15$$

$$a_2=a_1·r^{n-1}=15\cdot {4.2}^{2-1}=15\cdot {4.2}^1=15\cdot 4.2=63$$

$$a_3=a_1·r^{n-1}=15\cdot {4.2}^{3-1}=15\cdot {4.2}^2=15\cdot 17.64=264.6$$

$$a_4=a_1·r^{n-1}=15\cdot {4.2}^{4-1}=15\cdot {4.2}^3=15\cdot 74.08800000000001=1111.3200000000002$$

$$a_5=a_1·r^{n-1}=15\cdot {4.2}^{5-1}=15\cdot {4.2}^4=15\cdot 311.16960000000006=4667.544000000001$$

$$a_6=a_1·r^{n-1}=15\cdot {4.2}^{6-1}=15\cdot {4.2}^5=15\cdot 1306.9123200000004=19603.684800000006$$

$$a_7=a_1·r^{n-1}=15\cdot {4.2}^{7-1}=15\cdot {4.2}^6=15\cdot 5489.031744000002=82335.47616000002$$

$$a_8=a_1·r^{n-1}=15\cdot {4.2}^{8-1}=15\cdot {4.2}^7=15\cdot 23053.933324800008=345808.99987200013$$

$$a_9=a_1·r^{n-1}=15\cdot {4.2}^{9-1}=15\cdot {4.2}^8=15\cdot 96826.51996416003=1452397.7994624006$$

$$a_{10}=a_1·r^{n-1}=15\cdot {4.2}^{10-1}=15\cdot {4.2}^9=15\cdot 406671.38384947216=6100070.757742083$$