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：$$r=1.3125$$ 插入几何级数的公式：

$$a_1=64$$

$$a_2=a_1·r^{n-1}=64\cdot {1.3125}^{2-1}=64\cdot {1.3125}^1=64\cdot 1.3125=84$$

$$a_3=a_1·r^{n-1}=64\cdot {1.3125}^{3-1}=64\cdot {1.3125}^2=64\cdot 1.72265625=110.25$$

$$a_4=a_1·r^{n-1}=64\cdot {1.3125}^{4-1}=64\cdot {1.3125}^3=64\cdot 2.260986328125=144.703125$$

$$a_5=a_1·r^{n-1}=64\cdot {1.3125}^{5-1}=64\cdot {1.3125}^4=64\cdot 2.9675445556640625=189.9228515625$$

$$a_6=a_1·r^{n-1}=64\cdot {1.3125}^{6-1}=64\cdot {1.3125}^5=64\cdot 3.894902229309082=249.27374267578125$$

$$a_7=a_1·r^{n-1}=64\cdot {1.3125}^{7-1}=64\cdot {1.3125}^6=64\cdot 5.11205917596817=327.1717872619629$$

$$a_8=a_1·r^{n-1}=64\cdot {1.3125}^{8-1}=64\cdot {1.3125}^7=64\cdot 6.709577668458223=429.4129707813263$$

$$a_9=a_1·r^{n-1}=64\cdot {1.3125}^{9-1}=64\cdot {1.3125}^8=64\cdot 8.806320689851418=563.6045241504908$$

$$a_{10}=a_1·r^{n-1}=64\cdot {1.3125}^{10-1}=64\cdot {1.3125}^9=64\cdot 11.558295905429986=739.7309379475191$$