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：$$r=0.8947368421052632$$ 插入几何级数的公式：

$$a_1=38$$

$$a_2=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{2-1}=38\cdot {0.8947368421052632}^1=38\cdot 0.8947368421052632=34$$

$$a_3=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{3-1}=38\cdot {0.8947368421052632}^2=38\cdot 0.8005540166204986=30.42105263157895$$

$$a_4=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{4-1}=38\cdot {0.8947368421052632}^3=38\cdot 0.7162851727657094=27.218836565096957$$

$$a_5=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{5-1}=38\cdot {0.8947368421052632}^4=38\cdot 0.6408867335272136=24.353695874034116$$

$$a_6=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{6-1}=38\cdot {0.8947368421052632}^5=38\cdot 0.5734249721032963=21.79014893992526$$

$$a_7=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{7-1}=38\cdot {0.8947368421052632}^6=38\cdot 0.513064448724002=19.496449051512077$$

$$a_8=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{8-1}=38\cdot {0.8947368421052632}^7=38\cdot 0.4590576646477913=17.44419125661607$$

$$a_9=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{9-1}=38\cdot {0.8947368421052632}^8=38\cdot 0.4107358052111817=15.607960598024905$$

$$a_{10}=a_1·r^{n-1}=38\cdot {0.8947368421052632}^{10-1}=38\cdot {0.8947368421052632}^9=38\cdot 0.3675004572942152=13.965017377180178$$