解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=73$$ 和公比：$$r=0.7808219178082192$$ 插入几何级数的公式：

$$a_1=73$$

$$a_2=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{2-1}=73\cdot {0.7808219178082192}^1=73\cdot 0.7808219178082192=57$$

$$a_3=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{3-1}=73\cdot {0.7808219178082192}^2=73\cdot 0.6096828673297054=44.5068493150685$$

$$a_4=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{4-1}=73\cdot {0.7808219178082192}^3=73\cdot 0.47605374572319464=34.75192343779321$$

$$a_5=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{5-1}=73\cdot {0.7808219178082192}^4=73\cdot 0.3717131987153712=27.135063506222096$$

$$a_6=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{6-1}=73\cdot {0.7808219178082192}^5=73\cdot 0.29024181269556376=21.187652326776156$$

$$a_7=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{7-1}=73\cdot {0.7808219178082192}^6=73\cdot 0.22662716881708406=16.543783323647137$$

$$a_8=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{8-1}=73\cdot {0.7808219178082192}^7=73\cdot 0.17695546058320263=12.917748622573793$$

$$a_9=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{9-1}=73\cdot {0.7808219178082192}^8=73\cdot 0.138170702099213=10.086461253242549$$

$$a_{10}=a_1·r^{n-1}=73\cdot {0.7808219178082192}^{10-1}=73\cdot {0.7808219178082192}^9=73\cdot 0.10788671259801563=7.875730019655141$$