解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=360$$ 和公比：$$r=1.35$$ 插入几何级数的公式：

$$a_1=360$$

$$a_2=a_1·r^{n-1}=360\cdot {1.35}^{2-1}=360\cdot {1.35}^1=360\cdot 1.35=486.00000000000006$$

$$a_3=a_1·r^{n-1}=360\cdot {1.35}^{3-1}=360\cdot {1.35}^2=360\cdot 1.8225000000000002=656.1000000000001$$

$$a_4=a_1·r^{n-1}=360\cdot {1.35}^{4-1}=360\cdot {1.35}^3=360\cdot 2.4603750000000004=885.7350000000001$$

$$a_5=a_1·r^{n-1}=360\cdot {1.35}^{5-1}=360\cdot {1.35}^4=360\cdot 3.321506250000001=1195.7422500000005$$

$$a_6=a_1·r^{n-1}=360\cdot {1.35}^{6-1}=360\cdot {1.35}^5=360\cdot 4.484033437500002=1614.2520375000006$$

$$a_7=a_1·r^{n-1}=360\cdot {1.35}^{7-1}=360\cdot {1.35}^6=360\cdot 6.053445140625002=2179.240250625001$$

$$a_8=a_1·r^{n-1}=360\cdot {1.35}^{8-1}=360\cdot {1.35}^7=360\cdot 8.172150939843753=2941.9743383437512$$

$$a_9=a_1·r^{n-1}=360\cdot {1.35}^{9-1}=360\cdot {1.35}^8=360\cdot 11.032403768789068=3971.6653567640647$$

$$a_{10}=a_1·r^{n-1}=360\cdot {1.35}^{10-1}=360\cdot {1.35}^9=360\cdot 14.893745087865243=5361.748231631487$$