解答 - 幾何学的な数列

等比級数の一般形を求めるために、初項: $$a=42$$ と共通比数: $$r=1.7619047619047619$$ を数式に代入します。

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{2-1}=42\cdot {1.7619047619047619}^1=42\cdot 1.7619047619047619=74$$

$$a_3=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{3-1}=42\cdot {1.7619047619047619}^2=42\cdot 3.1043083900226756=130.38095238095238$$

$$a_4=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{4-1}=42\cdot {1.7619047619047619}^3=42\cdot 5.469495734801857=229.71882086167798$$

$$a_5=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{5-1}=42\cdot {1.7619047619047619}^4=42\cdot 9.636730580365176=404.74268437533743$$

$$a_6=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{6-1}=42\cdot {1.7619047619047619}^5=42\cdot 16.979001498738644=713.1180629470231$$

$$a_7=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{7-1}=42\cdot {1.7619047619047619}^6=42\cdot 29.915383593015704=1256.4461109066597$$

$$a_8=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{8-1}=42\cdot {1.7619047619047619}^7=42\cdot 52.70805680674195=2213.7383858831618$$

$$a_9=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{9-1}=42\cdot {1.7619047619047619}^8=42\cdot 92.86657627854534=3900.396203698904$$

$$a_{10}=a_1·r^{n-1}=42\cdot {1.7619047619047619}^{10-1}=42\cdot {1.7619047619047619}^9=42\cdot 163.62206296696084=6872.126644612355$$