解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=148$$ 和公比：$$r=1.054054054054054$$ 插入几何级数的公式：

$$a_1=148$$

$$a_2=a_1·r^{n-1}=148\cdot {1.054054054054054}^{2-1}=148\cdot {1.054054054054054}^1=148\cdot 1.054054054054054=155.99999999999997$$

$$a_3=a_1·r^{n-1}=148\cdot {1.054054054054054}^{3-1}=148\cdot {1.054054054054054}^2=148\cdot 1.1110299488677864=164.4324324324324$$

$$a_4=a_1·r^{n-1}=148\cdot {1.054054054054054}^{4-1}=148\cdot {1.054054054054054}^3=148\cdot 1.1710856217795587=173.32067202337467$$

$$a_5=a_1·r^{n-1}=148\cdot {1.054054054054054}^{5-1}=148\cdot {1.054054054054054}^4=148\cdot 1.2343875472811563=182.68935699761113$$

$$a_6=a_1·r^{n-1}=148\cdot {1.054054054054054}^{6-1}=148\cdot {1.054054054054054}^5=148\cdot 1.301111198485543=192.56445737586037$$

$$a_7=a_1·r^{n-1}=148\cdot {1.054054054054054}^{7-1}=148\cdot {1.054054054054054}^6=148\cdot 1.3714415335388155=202.9733469637447$$

$$a_8=a_1·r^{n-1}=148\cdot {1.054054054054054}^{8-1}=148\cdot {1.054054054054054}^7=148\cdot 1.4455735083246972=213.9448792320552$$

$$a_9=a_1·r^{n-1}=148\cdot {1.054054054054054}^{9-1}=148\cdot {1.054054054054054}^8=148\cdot 1.5237126168827888=225.50946729865274$$

$$a_{10}=a_1·r^{n-1}=148\cdot {1.054054054054054}^{10-1}=148\cdot {1.054054054054054}^9=148\cdot 1.606075461038615=237.69916823371503$$