解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=57$$ 和公比：$$r=2.3684210526315788$$ 插入几何级数的公式：

$$a_1=57$$

$$a_2=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{2-1}=57\cdot {2.3684210526315788}^1=57\cdot 2.3684210526315788=135$$

$$a_3=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{3-1}=57\cdot {2.3684210526315788}^2=57\cdot 5.609418282548476=319.7368421052631$$

$$a_4=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{4-1}=57\cdot {2.3684210526315788}^3=57\cdot 13.285464353404283=757.2714681440441$$

$$a_5=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{5-1}=57\cdot {2.3684210526315788}^4=57\cdot 31.46557346858909=1793.537687709578$$

$$a_6=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{6-1}=57\cdot {2.3684210526315788}^5=57\cdot 74.52372663613205=4247.852418259527$$

$$a_7=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{7-1}=57\cdot {2.3684210526315788}^6=57\cdot 176.50356308557588=10060.703095877825$$

$$a_8=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{8-1}=57\cdot {2.3684210526315788}^7=57\cdot 418.0347546763639=23827.98101655274$$

$$a_9=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{9-1}=57\cdot {2.3684210526315788}^8=57\cdot 990.0823137071776=56434.691881309125$$

$$a_{10}=a_1·r^{n-1}=57\cdot {2.3684210526315788}^{10-1}=57\cdot {2.3684210526315788}^9=57\cdot 2344.9317956222626=133661.11235046896$$