解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=75$$ 和公比：$$r=0.52$$ 插入几何级数的公式：

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {0.52}^{2-1}=75\cdot {0.52}^1=75\cdot 0.52=39$$

$$a_3=a_1·r^{n-1}=75\cdot {0.52}^{3-1}=75\cdot {0.52}^2=75\cdot 0.27040000000000003=20.28$$

$$a_4=a_1·r^{n-1}=75\cdot {0.52}^{4-1}=75\cdot {0.52}^3=75\cdot 0.140608=10.5456$$

$$a_5=a_1·r^{n-1}=75\cdot {0.52}^{5-1}=75\cdot {0.52}^4=75\cdot 0.07311616000000001=5.483712000000001$$

$$a_6=a_1·r^{n-1}=75\cdot {0.52}^{6-1}=75\cdot {0.52}^5=75\cdot 0.038020403200000004=2.85153024$$

$$a_7=a_1·r^{n-1}=75\cdot {0.52}^{7-1}=75\cdot {0.52}^6=75\cdot 0.019770609664000006=1.4827957248000003$$

$$a_8=a_1·r^{n-1}=75\cdot {0.52}^{8-1}=75\cdot {0.52}^7=75\cdot 0.010280717025280002=0.7710537768960002$$

$$a_9=a_1·r^{n-1}=75\cdot {0.52}^{9-1}=75\cdot {0.52}^8=75\cdot 0.005345972853145601=0.4009479639859201$$

$$a_{10}=a_1·r^{n-1}=75\cdot {0.52}^{10-1}=75\cdot {0.52}^9=75\cdot 0.002779905883635713=0.20849294127267845$$