解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=48$$ 和公比：$$r=0.875$$ 插入几何级数的公式：

$$a_1=48$$

$$a_2=a_1·r^{n-1}=48\cdot {0.875}^{2-1}=48\cdot {0.875}^1=48\cdot 0.875=42$$

$$a_3=a_1·r^{n-1}=48\cdot {0.875}^{3-1}=48\cdot {0.875}^2=48\cdot 0.765625=36.75$$

$$a_4=a_1·r^{n-1}=48\cdot {0.875}^{4-1}=48\cdot {0.875}^3=48\cdot 0.669921875=32.15625$$

$$a_5=a_1·r^{n-1}=48\cdot {0.875}^{5-1}=48\cdot {0.875}^4=48\cdot 0.586181640625=28.13671875$$

$$a_6=a_1·r^{n-1}=48\cdot {0.875}^{6-1}=48\cdot {0.875}^5=48\cdot 0.512908935546875=24.61962890625$$

$$a_7=a_1·r^{n-1}=48\cdot {0.875}^{7-1}=48\cdot {0.875}^6=48\cdot 0.4487953186035156=21.54217529296875$$

$$a_8=a_1·r^{n-1}=48\cdot {0.875}^{8-1}=48\cdot {0.875}^7=48\cdot 0.39269590377807617=18.849403381347656$$

$$a_9=a_1·r^{n-1}=48\cdot {0.875}^{9-1}=48\cdot {0.875}^8=48\cdot 0.34360891580581665=16.4932279586792$$

$$a_{10}=a_1·r^{n-1}=48\cdot {0.875}^{10-1}=48\cdot {0.875}^9=48\cdot 0.30065780133008957=14.4315744638443$$