解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=4$$ 和公比：$$r=36$$ 插入几何级数的公式：

$$a_1=4$$

$$a_2=a_1·r^{n-1}=4\cdot {36}^{2-1}=4\cdot {36}^1=4\cdot 36=144$$

$$a_3=a_1·r^{n-1}=4\cdot {36}^{3-1}=4\cdot {36}^2=4\cdot 1296=5184$$

$$a_4=a_1·r^{n-1}=4\cdot {36}^{4-1}=4\cdot {36}^3=4\cdot 46656=186624$$

$$a_5=a_1·r^{n-1}=4\cdot {36}^{5-1}=4\cdot {36}^4=4\cdot 1679616=6718464$$

$$a_6=a_1·r^{n-1}=4\cdot {36}^{6-1}=4\cdot {36}^5=4\cdot 60466176=241864704$$

$$a_7=a_1·r^{n-1}=4\cdot {36}^{7-1}=4\cdot {36}^6=4\cdot 2176782336=8707129344$$

$$a_8=a_1·r^{n-1}=4\cdot {36}^{8-1}=4\cdot {36}^7=4\cdot 78364164096=313456656384$$

$$a_9=a_1·r^{n-1}=4\cdot {36}^{9-1}=4\cdot {36}^8=4\cdot 2821109907456=11284439629824$$

$$a_{10}=a_1·r^{n-1}=4\cdot {36}^{10-1}=4\cdot {36}^9=4\cdot 101559956668416=406239826673664$$