解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=625$$ 和公比：$$r=0.52$$ 插入几何级数的公式：

$$a_1=625$$

$$a_2=a_1·r^{n-1}=625\cdot {0.52}^{2-1}=625\cdot {0.52}^1=625\cdot 0.52=325$$

$$a_3=a_1·r^{n-1}=625\cdot {0.52}^{3-1}=625\cdot {0.52}^2=625\cdot 0.27040000000000003=169.00000000000003$$

$$a_4=a_1·r^{n-1}=625\cdot {0.52}^{4-1}=625\cdot {0.52}^3=625\cdot 0.140608=87.88000000000001$$

$$a_5=a_1·r^{n-1}=625\cdot {0.52}^{5-1}=625\cdot {0.52}^4=625\cdot 0.07311616000000001=45.69760000000001$$

$$a_6=a_1·r^{n-1}=625\cdot {0.52}^{6-1}=625\cdot {0.52}^5=625\cdot 0.038020403200000004=23.762752000000003$$

$$a_7=a_1·r^{n-1}=625\cdot {0.52}^{7-1}=625\cdot {0.52}^6=625\cdot 0.019770609664000006=12.356631040000003$$

$$a_8=a_1·r^{n-1}=625\cdot {0.52}^{8-1}=625\cdot {0.52}^7=625\cdot 0.010280717025280002=6.425448140800001$$

$$a_9=a_1·r^{n-1}=625\cdot {0.52}^{9-1}=625\cdot {0.52}^8=625\cdot 0.005345972853145601=3.3412330332160005$$

$$a_{10}=a_1·r^{n-1}=625\cdot {0.52}^{10-1}=625\cdot {0.52}^9=625\cdot 0.002779905883635713=1.7374411772723206$$