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: $$a=75$$ と共通比数: $$r=0.6$$ を数式に代入します。

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {0.6}^{2-1}=75\cdot {0.6}^1=75\cdot 0.6=45$$

$$a_3=a_1·r^{n-1}=75\cdot {0.6}^{3-1}=75\cdot {0.6}^2=75\cdot 0.36=27$$

$$a_4=a_1·r^{n-1}=75\cdot {0.6}^{4-1}=75\cdot {0.6}^3=75\cdot 0.21599999999999997=16.2$$

$$a_5=a_1·r^{n-1}=75\cdot {0.6}^{5-1}=75\cdot {0.6}^4=75\cdot 0.1296=9.719999999999999$$

$$a_6=a_1·r^{n-1}=75\cdot {0.6}^{6-1}=75\cdot {0.6}^5=75\cdot 0.07775999999999998=5.831999999999999$$

$$a_7=a_1·r^{n-1}=75\cdot {0.6}^{7-1}=75\cdot {0.6}^6=75\cdot 0.04665599999999999=3.499199999999999$$

$$a_8=a_1·r^{n-1}=75\cdot {0.6}^{8-1}=75\cdot {0.6}^7=75\cdot 0.027993599999999993=2.0995199999999996$$

$$a_9=a_1·r^{n-1}=75\cdot {0.6}^{9-1}=75\cdot {0.6}^8=75\cdot 0.016796159999999994=1.2597119999999995$$

$$a_{10}=a_1·r^{n-1}=75\cdot {0.6}^{10-1}=75\cdot {0.6}^9=75\cdot 0.010077695999999997=0.7558271999999998$$