解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=13$$ 和公比：$$r=6.076923076923077$$ 插入几何级数的公式：

$$a_1=13$$

$$a_2=a_1·r^{n-1}=13\cdot {6.076923076923077}^{2-1}=13\cdot {6.076923076923077}^1=13\cdot 6.076923076923077=79$$

$$a_3=a_1·r^{n-1}=13\cdot {6.076923076923077}^{3-1}=13\cdot {6.076923076923077}^2=13\cdot 36.928994082840234=480.07692307692304$$

$$a_4=a_1·r^{n-1}=13\cdot {6.076923076923077}^{4-1}=13\cdot {6.076923076923077}^3=13\cdot 224.41465634956757=2917.3905325443784$$

$$a_5=a_1·r^{n-1}=13\cdot {6.076923076923077}^{5-1}=13\cdot {6.076923076923077}^4=13\cdot 1363.750603970449=17728.757851615836$$

$$a_6=a_1·r^{n-1}=13\cdot {6.076923076923077}^{6-1}=13\cdot {6.076923076923077}^5=13\cdot 8287.407516435806=107736.29771366547$$

$$a_7=a_1·r^{n-1}=13\cdot {6.076923076923077}^{7-1}=13\cdot {6.076923076923077}^6=13\cdot 50361.93798449451=654705.1937984286$$

$$a_8=a_1·r^{n-1}=13\cdot {6.076923076923077}^{8-1}=13\cdot {6.076923076923077}^7=13\cdot 306045.6231365435=3978593.1007750654$$

$$a_9=a_1·r^{n-1}=13\cdot {6.076923076923077}^{9-1}=13\cdot {6.076923076923077}^8=13\cdot 1859815.7098297644=24177604.227786936$$

$$a_{10}=a_1·r^{n-1}=13\cdot {6.076923076923077}^{10-1}=13\cdot {6.076923076923077}^9=13\cdot 11301957.005888568=146925441.07655138$$