解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=64$$ 和公比：$$r=1.75$$ 插入几何级数的公式：

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {1.75}^{2-1}=64\cdot {1.75}^1=64\cdot 1.75=112$$

$$a_3=a_1·r^{n-1}=64\cdot {1.75}^{3-1}=64\cdot {1.75}^2=64\cdot 3.0625=196$$

$$a_4=a_1·r^{n-1}=64\cdot {1.75}^{4-1}=64\cdot {1.75}^3=64\cdot 5.359375=343$$

$$a_5=a_1·r^{n-1}=64\cdot {1.75}^{5-1}=64\cdot {1.75}^4=64\cdot 9.37890625=600.25$$

$$a_6=a_1·r^{n-1}=64\cdot {1.75}^{6-1}=64\cdot {1.75}^5=64\cdot 16.4130859375=1050.4375$$

$$a_7=a_1·r^{n-1}=64\cdot {1.75}^{7-1}=64\cdot {1.75}^6=64\cdot 28.722900390625=1838.265625$$

$$a_8=a_1·r^{n-1}=64\cdot {1.75}^{8-1}=64\cdot {1.75}^7=64\cdot 50.26507568359375=3216.96484375$$

$$a_9=a_1·r^{n-1}=64\cdot {1.75}^{9-1}=64\cdot {1.75}^8=64\cdot 87.96388244628906=5629.6884765625$$

$$a_{10}=a_1·r^{n-1}=64\cdot {1.75}^{10-1}=64\cdot {1.75}^9=64\cdot 153.93679428100586=9851.954833984375$$