解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=200$$ 和公比：$$r=1.075$$ 插入几何级数的公式：

$$a_1=200$$

$$a_2=a_1·r^{n-1}=200\cdot {1.075}^{2-1}=200\cdot {1.075}^1=200\cdot 1.075=215$$

$$a_3=a_1·r^{n-1}=200\cdot {1.075}^{3-1}=200\cdot {1.075}^2=200\cdot 1.155625=231.12499999999997$$

$$a_4=a_1·r^{n-1}=200\cdot {1.075}^{4-1}=200\cdot {1.075}^3=200\cdot 1.2422968749999999=248.45937499999997$$

$$a_5=a_1·r^{n-1}=200\cdot {1.075}^{5-1}=200\cdot {1.075}^4=200\cdot 1.3354691406249999=267.09382812499996$$

$$a_6=a_1·r^{n-1}=200\cdot {1.075}^{6-1}=200\cdot {1.075}^5=200\cdot 1.4356293261718747=287.12586523437494$$

$$a_7=a_1·r^{n-1}=200\cdot {1.075}^{7-1}=200\cdot {1.075}^6=200\cdot 1.5433015256347653=308.66030512695306$$

$$a_8=a_1·r^{n-1}=200\cdot {1.075}^{8-1}=200\cdot {1.075}^7=200\cdot 1.6590491400573726=331.8098280114745$$

$$a_9=a_1·r^{n-1}=200\cdot {1.075}^{9-1}=200\cdot {1.075}^8=200\cdot 1.7834778255616754=356.6955651123351$$

$$a_{10}=a_1·r^{n-1}=200\cdot {1.075}^{10-1}=200\cdot {1.075}^9=200\cdot 1.917238662478801=383.4477324957602$$