解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=125$$ 和公比：$$r=1.92$$ 插入几何级数的公式：

$$a_1=125$$

$$a_2=a_1·r^{n-1}=125\cdot {1.92}^{2-1}=125\cdot {1.92}^1=125\cdot 1.92=240$$

$$a_3=a_1·r^{n-1}=125\cdot {1.92}^{3-1}=125\cdot {1.92}^2=125\cdot 3.6864=460.8$$

$$a_4=a_1·r^{n-1}=125\cdot {1.92}^{4-1}=125\cdot {1.92}^3=125\cdot 7.077887999999999=884.7359999999999$$

$$a_5=a_1·r^{n-1}=125\cdot {1.92}^{5-1}=125\cdot {1.92}^4=125\cdot 13.589544959999998=1698.6931199999997$$

$$a_6=a_1·r^{n-1}=125\cdot {1.92}^{6-1}=125\cdot {1.92}^5=125\cdot 26.091926323199996=3261.4907903999992$$

$$a_7=a_1·r^{n-1}=125\cdot {1.92}^{7-1}=125\cdot {1.92}^6=125\cdot 50.09649854054399=6262.062317567998$$

$$a_8=a_1·r^{n-1}=125\cdot {1.92}^{8-1}=125\cdot {1.92}^7=125\cdot 96.18527719784446=12023.159649730556$$

$$a_9=a_1·r^{n-1}=125\cdot {1.92}^{9-1}=125\cdot {1.92}^8=125\cdot 184.67573221986135=23084.46652748267$$

$$a_{10}=a_1·r^{n-1}=125\cdot {1.92}^{10-1}=125\cdot {1.92}^9=125\cdot 354.5774058621338=44322.17573276672$$