解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=67$$ 和公比：$$r=4.17910447761194$$ 插入几何级数的公式：

$$a_1=67$$

$$a_2=a_1·r^{n-1}=67\cdot {4.17910447761194}^{2-1}=67\cdot {4.17910447761194}^1=67\cdot 4.17910447761194=280$$

$$a_3=a_1·r^{n-1}=67\cdot {4.17910447761194}^{3-1}=67\cdot {4.17910447761194}^2=67\cdot 17.464914234796165=1170.1492537313432$$

$$a_4=a_1·r^{n-1}=67\cdot {4.17910447761194}^{4-1}=67\cdot {4.17910447761194}^3=67\cdot 72.98770127974517=4890.175985742926$$

$$a_5=a_1·r^{n-1}=67\cdot {4.17910447761194}^{5-1}=67\cdot {4.17910447761194}^4=67\cdot 305.02322922878574=20436.556358328646$$

$$a_6=a_1·r^{n-1}=67\cdot {4.17910447761194}^{6-1}=67\cdot {4.17910447761194}^5=67\cdot 1274.7239430456716=85406.50418406$$

$$a_7=a_1·r^{n-1}=67\cdot {4.17910447761194}^{7-1}=67\cdot {4.17910447761194}^6=67\cdot 5327.204538101313=356922.704052788$$

$$a_8=a_1·r^{n-1}=67\cdot {4.17910447761194}^{8-1}=67\cdot {4.17910447761194}^7=67\cdot 22262.944338333844=1491617.2706683676$$

$$a_9=a_1·r^{n-1}=67\cdot {4.17910447761194}^{9-1}=67\cdot {4.17910447761194}^8=67\cdot 93039.17036915636=6233624.414733476$$

$$a_{10}=a_1·r^{n-1}=67\cdot {4.17910447761194}^{10-1}=67\cdot {4.17910447761194}^9=67\cdot 388820.41348304146=26050967.703363776$$