解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=22$$ 和公比：$$r=1.0454545454545454$$ 插入几何级数的公式：

$$a_1=22$$

$$a_2=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{2-1}=22\cdot {1.0454545454545454}^1=22\cdot 1.0454545454545454=23$$

$$a_3=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{3-1}=22\cdot {1.0454545454545454}^2=22\cdot 1.09297520661157=24.045454545454543$$

$$a_4=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{4-1}=22\cdot {1.0454545454545454}^3=22\cdot 1.142655897821187=25.138429752066113$$

$$a_5=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{5-1}=22\cdot {1.0454545454545454}^4=22\cdot 1.1945948022676045=26.2810856498873$$

$$a_6=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{6-1}=22\cdot {1.0454545454545454}^5=22\cdot 1.248894566007041=27.4756804521549$$

$$a_7=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{7-1}=22\cdot {1.0454545454545454}^6=22\cdot 1.305662500825543=28.724575018161943$$

$$a_8=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{8-1}=22\cdot {1.0454545454545454}^7=22\cdot 1.3650107963176128=30.03023751898748$$

$$a_9=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{9-1}=22\cdot {1.0454545454545454}^8=22\cdot 1.427056741604777=31.395248315305096$$

$$a_{10}=a_1·r^{n-1}=22\cdot {1.0454545454545454}^{10-1}=22\cdot {1.0454545454545454}^9=22\cdot 1.491922957132267=32.822305056909876$$