解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=320$$ 和公比：$$r=2.25$$ 插入几何级数的公式：

$$a_1=320$$

$$a_2=a_1·r^{n-1}=320\cdot {2.25}^{2-1}=320\cdot {2.25}^1=320\cdot 2.25=720$$

$$a_3=a_1·r^{n-1}=320\cdot {2.25}^{3-1}=320\cdot {2.25}^2=320\cdot 5.0625=1620$$

$$a_4=a_1·r^{n-1}=320\cdot {2.25}^{4-1}=320\cdot {2.25}^3=320\cdot 11.390625=3645$$

$$a_5=a_1·r^{n-1}=320\cdot {2.25}^{5-1}=320\cdot {2.25}^4=320\cdot 25.62890625=8201.25$$

$$a_6=a_1·r^{n-1}=320\cdot {2.25}^{6-1}=320\cdot {2.25}^5=320\cdot 57.6650390625=18452.8125$$

$$a_7=a_1·r^{n-1}=320\cdot {2.25}^{7-1}=320\cdot {2.25}^6=320\cdot 129.746337890625=41518.828125$$

$$a_8=a_1·r^{n-1}=320\cdot {2.25}^{8-1}=320\cdot {2.25}^7=320\cdot 291.92926025390625=93417.36328125$$

$$a_9=a_1·r^{n-1}=320\cdot {2.25}^{9-1}=320\cdot {2.25}^8=320\cdot 656.8408355712891=210189.0673828125$$

$$a_{10}=a_1·r^{n-1}=320\cdot {2.25}^{10-1}=320\cdot {2.25}^9=320\cdot 1477.8918800354004=472925.4016113281$$