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：$$r=1.125$$ 插入几何级数的公式：

$$a_1=24$$

$$a_2=a_1·r^{n-1}=24\cdot {1.125}^{2-1}=24\cdot {1.125}^1=24\cdot 1.125=27$$

$$a_3=a_1·r^{n-1}=24\cdot {1.125}^{3-1}=24\cdot {1.125}^2=24\cdot 1.265625=30.375$$

$$a_4=a_1·r^{n-1}=24\cdot {1.125}^{4-1}=24\cdot {1.125}^3=24\cdot 1.423828125=34.171875$$

$$a_5=a_1·r^{n-1}=24\cdot {1.125}^{5-1}=24\cdot {1.125}^4=24\cdot 1.601806640625=38.443359375$$

$$a_6=a_1·r^{n-1}=24\cdot {1.125}^{6-1}=24\cdot {1.125}^5=24\cdot 1.802032470703125=43.248779296875$$

$$a_7=a_1·r^{n-1}=24\cdot {1.125}^{7-1}=24\cdot {1.125}^6=24\cdot 2.0272865295410156=48.654876708984375$$

$$a_8=a_1·r^{n-1}=24\cdot {1.125}^{8-1}=24\cdot {1.125}^7=24\cdot 2.2806973457336426=54.73673629760742$$

$$a_9=a_1·r^{n-1}=24\cdot {1.125}^{9-1}=24\cdot {1.125}^8=24\cdot 2.565784513950348=61.57882833480835$$

$$a_{10}=a_1·r^{n-1}=24\cdot {1.125}^{10-1}=24\cdot {1.125}^9=24\cdot 2.8865075781941414=69.2761818766594$$