解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=46$$ 和公比：$$r=1.3043478260869565$$ 插入几何级数的公式：

$$a_1=46$$

$$a_2=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{2-1}=46\cdot {1.3043478260869565}^1=46\cdot 1.3043478260869565=60$$

$$a_3=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{3-1}=46\cdot {1.3043478260869565}^2=46\cdot 1.7013232514177694=78.26086956521739$$

$$a_4=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{4-1}=46\cdot {1.3043478260869565}^3=46\cdot 2.21911728445796=102.07939508506617$$

$$a_5=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{5-1}=46\cdot {1.3043478260869565}^4=46\cdot 2.894500805814731=133.1470370674776$$

$$a_6=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{6-1}=46\cdot {1.3043478260869565}^5=46\cdot 3.775435833671388=173.67004834888382$$

$$a_7=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{7-1}=46\cdot {1.3043478260869565}^6=46\cdot 4.924481522180071=226.52615002028327$$

$$a_8=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{8-1}=46\cdot {1.3043478260869565}^7=46\cdot 6.4232367680609626=295.4688913308043$$

$$a_9=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{9-1}=46\cdot {1.3043478260869565}^8=46\cdot 8.378134914862125=385.39420608365776$$

$$a_{10}=a_1·r^{n-1}=46\cdot {1.3043478260869565}^{10-1}=46\cdot {1.3043478260869565}^9=46\cdot 10.928002062863643=502.68809489172753$$