解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=24$$ 和公比：$$r=1.75$$ 插入几何级数的公式：

$$a_1=24$$

$$a_2=a_1·r^{n-1}=24\cdot {1.75}^{2-1}=24\cdot {1.75}^1=24\cdot 1.75=42$$

$$a_3=a_1·r^{n-1}=24\cdot {1.75}^{3-1}=24\cdot {1.75}^2=24\cdot 3.0625=73.5$$

$$a_4=a_1·r^{n-1}=24\cdot {1.75}^{4-1}=24\cdot {1.75}^3=24\cdot 5.359375=128.625$$

$$a_5=a_1·r^{n-1}=24\cdot {1.75}^{5-1}=24\cdot {1.75}^4=24\cdot 9.37890625=225.09375$$

$$a_6=a_1·r^{n-1}=24\cdot {1.75}^{6-1}=24\cdot {1.75}^5=24\cdot 16.4130859375=393.9140625$$

$$a_7=a_1·r^{n-1}=24\cdot {1.75}^{7-1}=24\cdot {1.75}^6=24\cdot 28.722900390625=689.349609375$$

$$a_8=a_1·r^{n-1}=24\cdot {1.75}^{8-1}=24\cdot {1.75}^7=24\cdot 50.26507568359375=1206.36181640625$$

$$a_9=a_1·r^{n-1}=24\cdot {1.75}^{9-1}=24\cdot {1.75}^8=24\cdot 87.96388244628906=2111.1331787109375$$

$$a_{10}=a_1·r^{n-1}=24\cdot {1.75}^{10-1}=24\cdot {1.75}^9=24\cdot 153.93679428100586=3694.4830627441406$$