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：$$r=6.75$$ 插入几何级数的公式：

$$a_1=4$$

$$a_2=a_1·r^{n-1}=4\cdot {6.75}^{2-1}=4\cdot {6.75}^1=4\cdot 6.75=27$$

$$a_3=a_1·r^{n-1}=4\cdot {6.75}^{3-1}=4\cdot {6.75}^2=4\cdot 45.5625=182.25$$

$$a_4=a_1·r^{n-1}=4\cdot {6.75}^{4-1}=4\cdot {6.75}^3=4\cdot 307.546875=1230.1875$$

$$a_5=a_1·r^{n-1}=4\cdot {6.75}^{5-1}=4\cdot {6.75}^4=4\cdot 2075.94140625=8303.765625$$

$$a_6=a_1·r^{n-1}=4\cdot {6.75}^{6-1}=4\cdot {6.75}^5=4\cdot 14012.6044921875=56050.41796875$$

$$a_7=a_1·r^{n-1}=4\cdot {6.75}^{7-1}=4\cdot {6.75}^6=4\cdot 94585.08032226562=378340.3212890625$$

$$a_8=a_1·r^{n-1}=4\cdot {6.75}^{8-1}=4\cdot {6.75}^7=4\cdot 638449.292175293=2553797.168701172$$

$$a_9=a_1·r^{n-1}=4\cdot {6.75}^{9-1}=4\cdot {6.75}^8=4\cdot 4309532.722183228=17238130.88873291$$

$$a_{10}=a_1·r^{n-1}=4\cdot {6.75}^{10-1}=4\cdot {6.75}^9=4\cdot 29089345.874736786=116357383.49894714$$