解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=100$$ 和公比：$$r=6.25$$ 插入几何级数的公式：

$$a_1=100$$

$$a_2=a_1·r^{n-1}=100\cdot {6.25}^{2-1}=100\cdot {6.25}^1=100\cdot 6.25=625$$

$$a_3=a_1·r^{n-1}=100\cdot {6.25}^{3-1}=100\cdot {6.25}^2=100\cdot 39.0625=3906.25$$

$$a_4=a_1·r^{n-1}=100\cdot {6.25}^{4-1}=100\cdot {6.25}^3=100\cdot 244.140625=24414.0625$$

$$a_5=a_1·r^{n-1}=100\cdot {6.25}^{5-1}=100\cdot {6.25}^4=100\cdot 1525.87890625=152587.890625$$

$$a_6=a_1·r^{n-1}=100\cdot {6.25}^{6-1}=100\cdot {6.25}^5=100\cdot 9536.7431640625=953674.31640625$$

$$a_7=a_1·r^{n-1}=100\cdot {6.25}^{7-1}=100\cdot {6.25}^6=100\cdot 59604.644775390625=5960464.4775390625$$

$$a_8=a_1·r^{n-1}=100\cdot {6.25}^{8-1}=100\cdot {6.25}^7=100\cdot 372529.0298461914=37252902.98461914$$

$$a_9=a_1·r^{n-1}=100\cdot {6.25}^{9-1}=100\cdot {6.25}^8=100\cdot 2328306.4365386963=232830643.65386963$$

$$a_{10}=a_1·r^{n-1}=100\cdot {6.25}^{10-1}=100\cdot {6.25}^9=100\cdot 14551915.228366852=1455191522.8366852$$