解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=275$$ 和公比：$$r=0.52$$ 插入几何级数的公式：

$$a_1=275$$

$$a_2=a_1·r^{n-1}=275\cdot {0.52}^{2-1}=275\cdot {0.52}^1=275\cdot 0.52=143$$

$$a_3=a_1·r^{n-1}=275\cdot {0.52}^{3-1}=275\cdot {0.52}^2=275\cdot 0.27040000000000003=74.36000000000001$$

$$a_4=a_1·r^{n-1}=275\cdot {0.52}^{4-1}=275\cdot {0.52}^3=275\cdot 0.140608=38.6672$$

$$a_5=a_1·r^{n-1}=275\cdot {0.52}^{5-1}=275\cdot {0.52}^4=275\cdot 0.07311616000000001=20.106944000000002$$

$$a_6=a_1·r^{n-1}=275\cdot {0.52}^{6-1}=275\cdot {0.52}^5=275\cdot 0.038020403200000004=10.455610880000002$$

$$a_7=a_1·r^{n-1}=275\cdot {0.52}^{7-1}=275\cdot {0.52}^6=275\cdot 0.019770609664000006=5.436917657600001$$

$$a_8=a_1·r^{n-1}=275\cdot {0.52}^{8-1}=275\cdot {0.52}^7=275\cdot 0.010280717025280002=2.8271971819520005$$

$$a_9=a_1·r^{n-1}=275\cdot {0.52}^{9-1}=275\cdot {0.52}^8=275\cdot 0.005345972853145601=1.4701425346150403$$

$$a_{10}=a_1·r^{n-1}=275\cdot {0.52}^{10-1}=275\cdot {0.52}^9=275\cdot 0.002779905883635713=0.764474117999821$$