解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=77$$ 和公比：$$r=1.2727272727272727$$ 插入几何级数的公式：

$$a_1=77$$

$$a_2=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{2-1}=77\cdot {1.2727272727272727}^1=77\cdot 1.2727272727272727=98$$

$$a_3=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{3-1}=77\cdot {1.2727272727272727}^2=77\cdot 1.6198347107438016=124.72727272727272$$

$$a_4=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{4-1}=77\cdot {1.2727272727272727}^3=77\cdot 2.061607813673929=158.74380165289253$$

$$a_5=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{5-1}=77\cdot {1.2727272727272727}^4=77\cdot 2.6238644901304555=202.03756574004507$$

$$a_6=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{6-1}=77\cdot {1.2727272727272727}^5=77\cdot 3.3394638965296704=257.1387200327846$$

$$a_7=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{7-1}=77\cdot {1.2727272727272727}^6=77\cdot 4.250226777401399=327.2674618599077$$

$$a_8=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{8-1}=77\cdot {1.2727272727272727}^7=77\cdot 5.409379534874508=416.5222241853371$$

$$a_9=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{9-1}=77\cdot {1.2727272727272727}^8=77\cdot 6.884664862567555=530.1191944177017$$

$$a_{10}=a_1·r^{n-1}=77\cdot {1.2727272727272727}^{10-1}=77\cdot {1.2727272727272727}^9=77\cdot 8.762300734176888=674.6971565316204$$