解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=80$$ 和公比：$$r=2.75$$ 插入几何级数的公式：

$$a_1=80$$

$$a_2=a_1·r^{n-1}=80\cdot {2.75}^{2-1}=80\cdot {2.75}^1=80\cdot 2.75=220$$

$$a_3=a_1·r^{n-1}=80\cdot {2.75}^{3-1}=80\cdot {2.75}^2=80\cdot 7.5625=605$$

$$a_4=a_1·r^{n-1}=80\cdot {2.75}^{4-1}=80\cdot {2.75}^3=80\cdot 20.796875=1663.75$$

$$a_5=a_1·r^{n-1}=80\cdot {2.75}^{5-1}=80\cdot {2.75}^4=80\cdot 57.19140625=4575.3125$$

$$a_6=a_1·r^{n-1}=80\cdot {2.75}^{6-1}=80\cdot {2.75}^5=80\cdot 157.2763671875=12582.109375$$

$$a_7=a_1·r^{n-1}=80\cdot {2.75}^{7-1}=80\cdot {2.75}^6=80\cdot 432.510009765625=34600.80078125$$

$$a_8=a_1·r^{n-1}=80\cdot {2.75}^{8-1}=80\cdot {2.75}^7=80\cdot 1189.4025268554688=95152.2021484375$$

$$a_9=a_1·r^{n-1}=80\cdot {2.75}^{9-1}=80\cdot {2.75}^8=80\cdot 3270.856948852539=261668.55590820312$$

$$a_{10}=a_1·r^{n-1}=80\cdot {2.75}^{10-1}=80\cdot {2.75}^9=80\cdot 8994.856609344482=719588.5287475586$$