解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=20$$ 和公比：$$r=6.85$$ 插入几何级数的公式：

$$a_1=20$$

$$a_2=a_1·r^{n-1}=20\cdot {6.85}^{2-1}=20\cdot {6.85}^1=20\cdot 6.85=137$$

$$a_3=a_1·r^{n-1}=20\cdot {6.85}^{3-1}=20\cdot {6.85}^2=20\cdot 46.92249999999999=938.4499999999998$$

$$a_4=a_1·r^{n-1}=20\cdot {6.85}^{4-1}=20\cdot {6.85}^3=20\cdot 321.41912499999995=6428.382499999999$$

$$a_5=a_1·r^{n-1}=20\cdot {6.85}^{5-1}=20\cdot {6.85}^4=20\cdot 2201.7210062499994=44034.42012499999$$

$$a_6=a_1·r^{n-1}=20\cdot {6.85}^{6-1}=20\cdot {6.85}^5=20\cdot 15081.788892812496=301635.77785624994$$

$$a_7=a_1·r^{n-1}=20\cdot {6.85}^{7-1}=20\cdot {6.85}^6=20\cdot 103310.2539157656=2066205.078315312$$

$$a_8=a_1·r^{n-1}=20\cdot {6.85}^{8-1}=20\cdot {6.85}^7=20\cdot 707675.2393229943=14153504.786459886$$

$$a_9=a_1·r^{n-1}=20\cdot {6.85}^{9-1}=20\cdot {6.85}^8=20\cdot 4847575.38936251=96951507.7872502$$

$$a_{10}=a_1·r^{n-1}=20\cdot {6.85}^{10-1}=20\cdot {6.85}^9=20\cdot 33205891.417133197=664117828.342664$$