解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=12$$ 和公比：$$r=4.25$$ 插入几何级数的公式：

$$a_1=12$$

$$a_2=a_1·r^{n-1}=12\cdot {4.25}^{2-1}=12\cdot {4.25}^1=12\cdot 4.25=51$$

$$a_3=a_1·r^{n-1}=12\cdot {4.25}^{3-1}=12\cdot {4.25}^2=12\cdot 18.0625=216.75$$

$$a_4=a_1·r^{n-1}=12\cdot {4.25}^{4-1}=12\cdot {4.25}^3=12\cdot 76.765625=921.1875$$

$$a_5=a_1·r^{n-1}=12\cdot {4.25}^{5-1}=12\cdot {4.25}^4=12\cdot 326.25390625=3915.046875$$

$$a_6=a_1·r^{n-1}=12\cdot {4.25}^{6-1}=12\cdot {4.25}^5=12\cdot 1386.5791015625=16638.94921875$$

$$a_7=a_1·r^{n-1}=12\cdot {4.25}^{7-1}=12\cdot {4.25}^6=12\cdot 5892.961181640625=70715.5341796875$$

$$a_8=a_1·r^{n-1}=12\cdot {4.25}^{8-1}=12\cdot {4.25}^7=12\cdot 25045.085021972656=300541.0202636719$$

$$a_9=a_1·r^{n-1}=12\cdot {4.25}^{9-1}=12\cdot {4.25}^8=12\cdot 106441.61134338379=1277299.3361206055$$

$$a_{10}=a_1·r^{n-1}=12\cdot {4.25}^{10-1}=12\cdot {4.25}^9=12\cdot 452376.8482093811=5428522.178512573$$