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: $$a=123$$ と共通比数: $$r=2.4552845528455283$$ を数式に代入します。

$$a_1=123$$

$$a_2=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{2-1}=123\cdot {2.4552845528455283}^1=123\cdot 2.4552845528455283=302$$

$$a_3=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{3-1}=123\cdot {2.4552845528455283}^2=123\cdot 6.028422235441866=741.4959349593495$$

$$a_4=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{4-1}=123\cdot {2.4552845528455283}^3=123\cdot 14.801491992710922=1820.5835151034435$$

$$a_5=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{5-1}=123\cdot {2.4552845528455283}^4=123\cdot 36.3418746487699=4470.050581798698$$

$$a_6=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{6-1}=123\cdot {2.4552845528455283}^5=123\cdot 89.22964344657325=10975.246143928509$$

$$a_7=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{7-1}=123\cdot {2.4552845528455283}^6=123\cdot 219.0841652102855=26947.352320865117$$

$$a_8=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{8-1}=123\cdot {2.4552845528455283}^7=123\cdot 537.9139666138717=66163.41789350622$$

$$a_9=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{9-1}=123\cdot {2.4552845528455283}^8=123\cdot 1320.7318529869044=162450.01791738925$$

$$a_{10}=a_1·r^{n-1}=123\cdot {2.4552845528455283}^{10-1}=123\cdot {2.4552845528455283}^9=123\cdot 3242.7725170897975=398861.01960204507$$