解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=65$$ 和公比：$$r=1.8615384615384616$$ 插入几何级数的公式：

$$a_1=65$$

$$a_2=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{2-1}=65\cdot {1.8615384615384616}^1=65\cdot 1.8615384615384616=121$$

$$a_3=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{3-1}=65\cdot {1.8615384615384616}^2=65\cdot 3.4653254437869823=225.24615384615385$$

$$a_4=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{4-1}=65\cdot {1.8615384615384616}^3=65\cdot 6.4508365953573055=419.30437869822487$$

$$a_5=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{5-1}=65\cdot {1.8615384615384616}^4=65\cdot 12.008480431357446=780.5512280382341$$

$$a_6=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{6-1}=65\cdot {1.8615384615384616}^5=65\cdot 22.35424818760386=1453.026132194251$$

$$a_7=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{7-1}=65\cdot {1.8615384615384616}^6=65\cdot 41.61329278000104=2704.8640307000674$$

$$a_8=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{8-1}=65\cdot {1.8615384615384616}^7=65\cdot 77.4647450212327=5035.208426380125$$

$$a_9=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{9-1}=65\cdot {1.8615384615384616}^8=65\cdot 144.20360227029474=9373.234147569157$$

$$a_{10}=a_1·r^{n-1}=65\cdot {1.8615384615384616}^{10-1}=65\cdot {1.8615384615384616}^9=65\cdot 268.44055191854864=17448.635874705662$$