解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=500$$ 和公比：$$r=0.88$$ 插入几何级数的公式：

$$a_1=500$$

$$a_2=a_1·r^{n-1}=500\cdot {0.88}^{2-1}=500\cdot {0.88}^1=500\cdot 0.88=440$$

$$a_3=a_1·r^{n-1}=500\cdot {0.88}^{3-1}=500\cdot {0.88}^2=500\cdot 0.7744=387.2$$

$$a_4=a_1·r^{n-1}=500\cdot {0.88}^{4-1}=500\cdot {0.88}^3=500\cdot 0.681472=340.736$$

$$a_5=a_1·r^{n-1}=500\cdot {0.88}^{5-1}=500\cdot {0.88}^4=500\cdot 0.59969536=299.84768$$

$$a_6=a_1·r^{n-1}=500\cdot {0.88}^{6-1}=500\cdot {0.88}^5=500\cdot 0.5277319168=263.8659584$$

$$a_7=a_1·r^{n-1}=500\cdot {0.88}^{7-1}=500\cdot {0.88}^6=500\cdot 0.464404086784=232.202043392$$

$$a_8=a_1·r^{n-1}=500\cdot {0.88}^{8-1}=500\cdot {0.88}^7=500\cdot 0.40867559636992=204.33779818496$$

$$a_9=a_1·r^{n-1}=500\cdot {0.88}^{9-1}=500\cdot {0.88}^8=500\cdot 0.3596345248055296=179.8172624027648$$

$$a_{10}=a_1·r^{n-1}=500\cdot {0.88}^{10-1}=500\cdot {0.88}^9=500\cdot 0.31647838182886606=158.23919091443304$$