解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=38$$ 和公比：$$r=1.5526315789473684$$ 插入几何级数的公式：

$$a_1=38$$

$$a_2=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{2-1}=38\cdot {1.5526315789473684}^1=38\cdot 1.5526315789473684=59$$

$$a_3=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{3-1}=38\cdot {1.5526315789473684}^2=38\cdot 2.410664819944598=91.60526315789473$$

$$a_4=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{4-1}=38\cdot {1.5526315789473684}^3=38\cdot 3.742874325703455=142.22922437673128$$

$$a_5=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{5-1}=38\cdot {1.5526315789473684}^4=38\cdot 5.811304874118522=220.82958521650386$$

$$a_6=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{6-1}=38\cdot {1.5526315789473684}^5=38\cdot 9.022815462447179=342.8669875729928$$

$$a_7=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{7-1}=38\cdot {1.5526315789473684}^6=38\cdot 14.009108218010093=532.3461122843835$$

$$a_8=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{8-1}=38\cdot {1.5526315789473684}^7=38\cdot 21.750983812173562=826.5373848625953$$

$$a_9=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{9-1}=38\cdot {1.5526315789473684}^8=38\cdot 33.77126433995369=1283.3080449182403$$

$$a_{10}=a_1·r^{n-1}=38\cdot {1.5526315789473684}^{10-1}=38\cdot {1.5526315789473684}^9=38\cdot 52.43433147519125=1992.5045960572675$$