解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=364$$ 和公比：$$r=2.75$$ 插入几何级数的公式：

$$a_1=364$$

$$a_2=a_1·r^{n-1}=364\cdot {2.75}^{2-1}=364\cdot {2.75}^1=364\cdot 2.75=1001$$

$$a_3=a_1·r^{n-1}=364\cdot {2.75}^{3-1}=364\cdot {2.75}^2=364\cdot 7.5625=2752.75$$

$$a_4=a_1·r^{n-1}=364\cdot {2.75}^{4-1}=364\cdot {2.75}^3=364\cdot 20.796875=7570.0625$$

$$a_5=a_1·r^{n-1}=364\cdot {2.75}^{5-1}=364\cdot {2.75}^4=364\cdot 57.19140625=20817.671875$$

$$a_6=a_1·r^{n-1}=364\cdot {2.75}^{6-1}=364\cdot {2.75}^5=364\cdot 157.2763671875=57248.59765625$$

$$a_7=a_1·r^{n-1}=364\cdot {2.75}^{7-1}=364\cdot {2.75}^6=364\cdot 432.510009765625=157433.6435546875$$

$$a_8=a_1·r^{n-1}=364\cdot {2.75}^{8-1}=364\cdot {2.75}^7=364\cdot 1189.4025268554688=432942.5197753906$$

$$a_9=a_1·r^{n-1}=364\cdot {2.75}^{9-1}=364\cdot {2.75}^8=364\cdot 3270.856948852539=1190591.9293823242$$

$$a_{10}=a_1·r^{n-1}=364\cdot {2.75}^{10-1}=364\cdot {2.75}^9=364\cdot 8994.856609344482=3274127.8058013916$$