解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=154$$ 和公比：$$r=1.6363636363636365$$ 插入几何级数的公式：

$$a_1=154$$

$$a_2=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{2-1}=154\cdot {1.6363636363636365}^1=154\cdot 1.6363636363636365=252.00000000000003$$

$$a_3=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{3-1}=154\cdot {1.6363636363636365}^2=154\cdot 2.6776859504132235=412.36363636363643$$

$$a_4=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{4-1}=154\cdot {1.6363636363636365}^3=154\cdot 4.381667918858002=674.7768595041324$$

$$a_5=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{5-1}=154\cdot {1.6363636363636365}^4=154\cdot 7.1700020490403675=1104.1803155522166$$

$$a_6=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{6-1}=154\cdot {1.6363636363636365}^5=154\cdot 11.732730625702422=1806.8405163581729$$

$$a_7=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{7-1}=154\cdot {1.6363636363636365}^6=154\cdot 19.199013751149415=2956.64811767701$$

$$a_8=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{8-1}=154\cdot {1.6363636363636365}^7=154\cdot 31.41656795642632=4838.151465289653$$

$$a_9=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{9-1}=154\cdot {1.6363636363636365}^8=154\cdot 51.40892938324308=7916.975125019434$$

$$a_{10}=a_1·r^{n-1}=154\cdot {1.6363636363636365}^{10-1}=154\cdot {1.6363636363636365}^9=154\cdot 84.12370262712504=12955.050204577255$$