解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=19$$ 和公比：$$r=1.105263157894737$$ 插入几何级数的公式：

$$a_1=19$$

$$a_2=a_1·r^{n-1}=19\cdot {1.105263157894737}^{2-1}=19\cdot {1.105263157894737}^1=19\cdot 1.105263157894737=21.000000000000004$$

$$a_3=a_1·r^{n-1}=19\cdot {1.105263157894737}^{3-1}=19\cdot {1.105263157894737}^2=19\cdot 1.2216066481994463=23.21052631578948$$

$$a_4=a_1·r^{n-1}=19\cdot {1.105263157894737}^{4-1}=19\cdot {1.105263157894737}^3=19\cdot 1.350196821694125=25.653739612188375$$

$$a_5=a_1·r^{n-1}=19\cdot {1.105263157894737}^{5-1}=19\cdot {1.105263157894737}^4=19\cdot 1.4923228029250855=28.354133255576624$$

$$a_6=a_1·r^{n-1}=19\cdot {1.105263157894737}^{6-1}=19\cdot {1.105263157894737}^5=19\cdot 1.6494094137593052=31.3387788614268$$

$$a_7=a_1·r^{n-1}=19\cdot {1.105263157894737}^{7-1}=19\cdot {1.105263157894737}^6=19\cdot 1.8230314573129165=34.63759768894541$$

$$a_8=a_1·r^{n-1}=19\cdot {1.105263157894737}^{8-1}=19\cdot {1.105263157894737}^7=19\cdot 2.0149295054511183=38.28366060357125$$

$$a_9=a_1·r^{n-1}=19\cdot {1.105263157894737}^{9-1}=19\cdot {1.105263157894737}^8=19\cdot 2.227027348130184=42.31351961447349$$

$$a_{10}=a_1·r^{n-1}=19\cdot {1.105263157894737}^{10-1}=19\cdot {1.105263157894737}^9=19\cdot 2.4614512795123087=46.76757431073386$$