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：$$r=1.265625$$ 插入几何级数的公式：

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {1.265625}^{2-1}=64\cdot {1.265625}^1=64\cdot 1.265625=81$$

$$a_3=a_1·r^{n-1}=64\cdot {1.265625}^{3-1}=64\cdot {1.265625}^2=64\cdot 1.601806640625=102.515625$$

$$a_4=a_1·r^{n-1}=64\cdot {1.265625}^{4-1}=64\cdot {1.265625}^3=64\cdot 2.0272865295410156=129.746337890625$$

$$a_5=a_1·r^{n-1}=64\cdot {1.265625}^{5-1}=64\cdot {1.265625}^4=64\cdot 2.565784513950348=164.21020889282227$$

$$a_6=a_1·r^{n-1}=64\cdot {1.265625}^{6-1}=64\cdot {1.265625}^5=64\cdot 3.247321025468409=207.82854562997818$$

$$a_7=a_1·r^{n-1}=64\cdot {1.265625}^{7-1}=64\cdot {1.265625}^6=64\cdot 4.109890672858455=263.03300306294113$$

$$a_8=a_1·r^{n-1}=64\cdot {1.265625}^{8-1}=64\cdot {1.265625}^7=64\cdot 5.201580382836482=332.9011445015349$$

$$a_9=a_1·r^{n-1}=64\cdot {1.265625}^{9-1}=64\cdot {1.265625}^8=64\cdot 6.583250172027423=421.3280110097551$$

$$a_{10}=a_1·r^{n-1}=64\cdot {1.265625}^{10-1}=64\cdot {1.265625}^9=64\cdot 8.331925998972208=533.2432639342213$$