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: $$a=111$$ と共通比数: $$r=72.09009009009009$$ を数式に代入します。

$$a_1=111$$

$$a_2=a_1·r^{n-1}=111\cdot {72.09009009009009}^{2-1}=111\cdot {72.09009009009009}^1=111\cdot 72.09009009009009=8002$$

$$a_3=a_1·r^{n-1}=111\cdot {72.09009009009009}^{3-1}=111\cdot {72.09009009009009}^2=111\cdot 5196.981089197305=576864.9009009008$$

$$a_4=a_1·r^{n-1}=111\cdot {72.09009009009009}^{4-1}=111\cdot {72.09009009009009}^3=111\cdot 374650.8349167282=41586242.67575683$$

$$a_5=a_1·r^{n-1}=111\cdot {72.09009009009009}^{5-1}=111\cdot {72.09009009009009}^4=111\cdot 27008612.441474404=2997955981.003659$$

$$a_6=a_1·r^{n-1}=111\cdot {72.09009009009009}^{6-1}=111\cdot {72.09009009009009}^5=111\cdot 1947053304.1142178=216122916756.67816$$

$$a_7=a_1·r^{n-1}=111\cdot {72.09009009009009}^{7-1}=111\cdot {72.09009009009009}^6=111\cdot 140363248103.80154=15580320539521.97$$

$$a_8=a_1·r^{n-1}=111\cdot {72.09009009009009}^{8-1}=111\cdot {72.09009009009009}^7=111\cdot 10118799201140.719=1123186711326619.8$$

$$a_9=a_1·r^{n-1}=111\cdot {72.09009009009009}^{9-1}=111\cdot {72.09009009009009}^8=111\cdot 729465146013766=80970631207528030$$

$$a_{10}=a_1·r^{n-1}=111\cdot {72.09009009009009}^{10-1}=111\cdot {72.09009009009009}^9=111\cdot 52587208093713110=5.837180098402156E+18$$