解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=56$$ 和公比：$$r=1.4464285714285714$$ 插入几何级数的公式：

$$a_1=56$$

$$a_2=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{2-1}=56\cdot {1.4464285714285714}^1=56\cdot 1.4464285714285714=81$$

$$a_3=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{3-1}=56\cdot {1.4464285714285714}^2=56\cdot 2.092155612244898=117.16071428571428$$

$$a_4=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{4-1}=56\cdot {1.4464285714285714}^3=56\cdot 3.0261536534256557=169.46460459183672$$

$$a_5=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{5-1}=56\cdot {1.4464285714285714}^4=56\cdot 4.377115105847824=245.11844592747812$$

$$a_6=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{6-1}=56\cdot {1.4464285714285714}^5=56\cdot 6.331184349529887=354.5463235736737$$

$$a_7=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{7-1}=56\cdot {1.4464285714285714}^6=56\cdot 9.157605934141444=512.8259323119208$$

$$a_8=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{8-1}=56\cdot {1.4464285714285714}^7=56\cdot 13.245822869026016=741.7660806654569$$

$$a_9=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{9-1}=56\cdot {1.4464285714285714}^8=56\cdot 19.1591366498412=1072.9116523911073$$

$$a_{10}=a_1·r^{n-1}=56\cdot {1.4464285714285714}^{10-1}=56\cdot {1.4464285714285714}^9=56\cdot 27.712322654234598=1551.8900686371376$$