解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=23$$ 和公比：$$r=1.9565217391304348$$ 插入几何级数的公式：

$$a_1=23$$

$$a_2=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{2-1}=23\cdot {1.9565217391304348}^1=23\cdot 1.9565217391304348=45$$

$$a_3=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{3-1}=23\cdot {1.9565217391304348}^2=23\cdot 3.827977315689981=88.04347826086956$$

$$a_4=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{4-1}=23\cdot {1.9565217391304348}^3=23\cdot 7.4895208350456155=172.25897920604916$$

$$a_5=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{5-1}=23\cdot {1.9565217391304348}^4=23\cdot 14.653410329437074=337.0284375770527$$

$$a_6=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{6-1}=23\cdot {1.9565217391304348}^5=23\cdot 28.6697158619421=659.4034648246684$$

$$a_7=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{7-1}=23\cdot {1.9565217391304348}^6=23\cdot 56.092922338582376=1290.1372137873946$$

$$a_8=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{8-1}=23\cdot {1.9565217391304348}^7=23\cdot 109.7470219667916=2524.181505236207$$

$$a_9=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{9-1}=23\cdot {1.9565217391304348}^8=23\cdot 214.72243428285313=4938.615988505622$$

$$a_{10}=a_1·r^{n-1}=23\cdot {1.9565217391304348}^{10-1}=23\cdot {1.9565217391304348}^9=23\cdot 420.1091105534083=9662.50954272839$$