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: $$r=1.7857142857142858$$ を数式に代入します。

$$a_1=42$$

$$a_2=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{2-1}=42\cdot {1.7857142857142858}^1=42\cdot 1.7857142857142858=75$$

$$a_3=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{3-1}=42\cdot {1.7857142857142858}^2=42\cdot 3.188775510204082=133.92857142857144$$

$$a_4=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{4-1}=42\cdot {1.7857142857142858}^3=42\cdot 5.69424198250729=239.15816326530617$$

$$a_5=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{5-1}=42\cdot {1.7857142857142858}^4=42\cdot 10.168289254477303=427.06814868804673$$

$$a_6=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{6-1}=42\cdot {1.7857142857142858}^5=42\cdot 18.157659382995185=762.6216940857978$$

$$a_7=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{7-1}=42\cdot {1.7857142857142858}^6=42\cdot 32.424391755348545=1361.824453724639$$

$$a_8=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{8-1}=42\cdot {1.7857142857142858}^7=42\cdot 57.90069956312241=2431.8293816511414$$

$$a_9=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{9-1}=42\cdot {1.7857142857142858}^8=42\cdot 103.39410636271859=4342.552467234181$$

$$a_{10}=a_1·r^{n-1}=42\cdot {1.7857142857142858}^{10-1}=42\cdot {1.7857142857142858}^9=42\cdot 184.63233279056894=7754.5579772038955$$