解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=5$$ 和公比：$$r=10.6$$ 插入几何级数的公式：

$$a_1=5$$

$$a_2=a_1·r^{n-1}=5\cdot {10.6}^{2-1}=5\cdot {10.6}^1=5\cdot 10.6=53$$

$$a_3=a_1·r^{n-1}=5\cdot {10.6}^{3-1}=5\cdot {10.6}^2=5\cdot 112.36=561.8$$

$$a_4=a_1·r^{n-1}=5\cdot {10.6}^{4-1}=5\cdot {10.6}^3=5\cdot 1191.0159999999998=5955.079999999999$$

$$a_5=a_1·r^{n-1}=5\cdot {10.6}^{5-1}=5\cdot {10.6}^4=5\cdot 12624.769599999998=63123.84799999999$$

$$a_6=a_1·r^{n-1}=5\cdot {10.6}^{6-1}=5\cdot {10.6}^5=5\cdot 133822.55775999997=669112.7887999999$$

$$a_7=a_1·r^{n-1}=5\cdot {10.6}^{7-1}=5\cdot {10.6}^6=5\cdot 1418519.1122559998=7092595.561279999$$

$$a_8=a_1·r^{n-1}=5\cdot {10.6}^{8-1}=5\cdot {10.6}^7=5\cdot 15036302.589913597=75181512.94956799$$

$$a_9=a_1·r^{n-1}=5\cdot {10.6}^{9-1}=5\cdot {10.6}^8=5\cdot 159384807.4530841=796924037.2654206$$

$$a_{10}=a_1·r^{n-1}=5\cdot {10.6}^{10-1}=5\cdot {10.6}^9=5\cdot 1689478959.0026915=8447394795.013457$$