解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=78$$ 和公比：$$r=6.8076923076923075$$ 插入几何级数的公式：

$$a_1=78$$

$$a_2=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{2-1}=78\cdot {6.8076923076923075}^1=78\cdot 6.8076923076923075=531$$

$$a_3=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{3-1}=78\cdot {6.8076923076923075}^2=78\cdot 46.344674556213015=3614.8846153846152$$

$$a_4=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{4-1}=78\cdot {6.8076923076923075}^3=78\cdot 315.50028447883477=24609.02218934911$$

$$a_5=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{5-1}=78\cdot {6.8076923076923075}^4=78\cdot 2147.828859721298=167530.65105826125$$

$$a_6=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{6-1}=78\cdot {6.8076923076923075}^5=78\cdot 14621.758006564221=1140497.1245120093$$

$$a_7=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{7-1}=78\cdot {6.8076923076923075}^6=78\cdot 99540.42950622566=7764153.501485601$$

$$a_8=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{8-1}=78\cdot {6.8076923076923075}^7=78\cdot 677640.6162539207=52855968.06780582$$

$$a_9=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{9-1}=78\cdot {6.8076923076923075}^8=78\cdot 4613168.810651692=359827167.2308319$$

$$a_{10}=a_1·r^{n-1}=78\cdot {6.8076923076923075}^{10-1}=78\cdot {6.8076923076923075}^9=78\cdot 31405033.82635959=2449592638.456048$$