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: $$r=1.1904761904761905$$ を数式に代入します。

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{2-1}=42\cdot {1.1904761904761905}^1=42\cdot 1.1904761904761905=50$$

$$a_3=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{3-1}=42\cdot {1.1904761904761905}^2=42\cdot 1.417233560090703=59.52380952380952$$

$$a_4=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{4-1}=42\cdot {1.1904761904761905}^3=42\cdot 1.6871828096317891=70.86167800453515$$

$$a_5=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{5-1}=42\cdot {1.1904761904761905}^4=42\cdot 2.008550963847368=84.35914048158946$$

$$a_6=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{6-1}=42\cdot {1.1904761904761905}^5=42\cdot 2.391132099818295=100.4275481923684$$

$$a_7=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{7-1}=42\cdot {1.1904761904761905}^6=42\cdot 2.846585833117018=119.55660499091476$$

$$a_8=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{8-1}=42\cdot {1.1904761904761905}^7=42\cdot 3.3887926584726404=142.3292916558509$$

$$a_9=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{9-1}=42\cdot {1.1904761904761905}^8=42\cdot 4.034276974372191=169.43963292363202$$

$$a_{10}=a_1·r^{n-1}=42\cdot {1.1904761904761905}^{10-1}=42\cdot {1.1904761904761905}^9=42\cdot 4.802710683776418=201.71384871860954$$