解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=15$$ 和公比：$$r=1.2$$ 插入几何级数的公式：

$$a_1=15$$

$$a_2=a_1·r^{n-1}=15\cdot {1.2}^{2-1}=15\cdot {1.2}^1=15\cdot 1.2=18$$

$$a_3=a_1·r^{n-1}=15\cdot {1.2}^{3-1}=15\cdot {1.2}^2=15\cdot 1.44=21.599999999999998$$

$$a_4=a_1·r^{n-1}=15\cdot {1.2}^{4-1}=15\cdot {1.2}^3=15\cdot 1.7279999999999998=25.919999999999995$$

$$a_5=a_1·r^{n-1}=15\cdot {1.2}^{5-1}=15\cdot {1.2}^4=15\cdot 2.0736=31.104$$

$$a_6=a_1·r^{n-1}=15\cdot {1.2}^{6-1}=15\cdot {1.2}^5=15\cdot 2.4883199999999994=37.32479999999999$$

$$a_7=a_1·r^{n-1}=15\cdot {1.2}^{7-1}=15\cdot {1.2}^6=15\cdot 2.9859839999999993=44.78975999999999$$

$$a_8=a_1·r^{n-1}=15\cdot {1.2}^{8-1}=15\cdot {1.2}^7=15\cdot 3.583180799999999=53.747711999999986$$

$$a_9=a_1·r^{n-1}=15\cdot {1.2}^{9-1}=15\cdot {1.2}^8=15\cdot 4.2998169599999985=64.49725439999997$$

$$a_{10}=a_1·r^{n-1}=15\cdot {1.2}^{10-1}=15\cdot {1.2}^9=15\cdot 5.1597803519999985=77.39670527999998$$