解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=48$$ 和公比：$$r=1.125$$ 插入几何级数的公式：

$$a_1=48$$

$$a_2=a_1·r^{n-1}=48\cdot {1.125}^{2-1}=48\cdot {1.125}^1=48\cdot 1.125=54$$

$$a_3=a_1·r^{n-1}=48\cdot {1.125}^{3-1}=48\cdot {1.125}^2=48\cdot 1.265625=60.75$$

$$a_4=a_1·r^{n-1}=48\cdot {1.125}^{4-1}=48\cdot {1.125}^3=48\cdot 1.423828125=68.34375$$

$$a_5=a_1·r^{n-1}=48\cdot {1.125}^{5-1}=48\cdot {1.125}^4=48\cdot 1.601806640625=76.88671875$$

$$a_6=a_1·r^{n-1}=48\cdot {1.125}^{6-1}=48\cdot {1.125}^5=48\cdot 1.802032470703125=86.49755859375$$

$$a_7=a_1·r^{n-1}=48\cdot {1.125}^{7-1}=48\cdot {1.125}^6=48\cdot 2.0272865295410156=97.30975341796875$$

$$a_8=a_1·r^{n-1}=48\cdot {1.125}^{8-1}=48\cdot {1.125}^7=48\cdot 2.2806973457336426=109.47347259521484$$

$$a_9=a_1·r^{n-1}=48\cdot {1.125}^{9-1}=48\cdot {1.125}^8=48\cdot 2.565784513950348=123.1576566696167$$

$$a_{10}=a_1·r^{n-1}=48\cdot {1.125}^{10-1}=48\cdot {1.125}^9=48\cdot 2.8865075781941414=138.5523637533188$$