解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=4$$ 和公比：$$r=13.25$$ 插入几何级数的公式：

$$a_1=4$$

$$a_2=a_1·r^{n-1}=4\cdot {13.25}^{2-1}=4\cdot {13.25}^1=4\cdot 13.25=53$$

$$a_3=a_1·r^{n-1}=4\cdot {13.25}^{3-1}=4\cdot {13.25}^2=4\cdot 175.5625=702.25$$

$$a_4=a_1·r^{n-1}=4\cdot {13.25}^{4-1}=4\cdot {13.25}^3=4\cdot 2326.203125=9304.8125$$

$$a_5=a_1·r^{n-1}=4\cdot {13.25}^{5-1}=4\cdot {13.25}^4=4\cdot 30822.19140625=123288.765625$$

$$a_6=a_1·r^{n-1}=4\cdot {13.25}^{6-1}=4\cdot {13.25}^5=4\cdot 408394.0361328125=1633576.14453125$$

$$a_7=a_1·r^{n-1}=4\cdot {13.25}^{7-1}=4\cdot {13.25}^6=4\cdot 5411220.978759766=21644883.915039062$$

$$a_8=a_1·r^{n-1}=4\cdot {13.25}^{8-1}=4\cdot {13.25}^7=4\cdot 71698677.9685669=286794711.8742676$$

$$a_9=a_1·r^{n-1}=4\cdot {13.25}^{9-1}=4\cdot {13.25}^8=4\cdot 950007483.0835114=3800029932.3340454$$

$$a_{10}=a_1·r^{n-1}=4\cdot {13.25}^{10-1}=4\cdot {13.25}^9=4\cdot 12587599150.856525=50350396603.4261$$