解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=75$$ 和公比：$$r=1.08$$ 插入几何级数的公式：

$$a_1=75$$

$$a_2=a_1·r^{n-1}=75\cdot {1.08}^{2-1}=75\cdot {1.08}^1=75\cdot 1.08=81$$

$$a_3=a_1·r^{n-1}=75\cdot {1.08}^{3-1}=75\cdot {1.08}^2=75\cdot 1.1664=87.48$$

$$a_4=a_1·r^{n-1}=75\cdot {1.08}^{4-1}=75\cdot {1.08}^3=75\cdot 1.2597120000000002=94.47840000000001$$

$$a_5=a_1·r^{n-1}=75\cdot {1.08}^{5-1}=75\cdot {1.08}^4=75\cdot 1.3604889600000003=102.03667200000002$$

$$a_6=a_1·r^{n-1}=75\cdot {1.08}^{6-1}=75\cdot {1.08}^5=75\cdot 1.4693280768000005=110.19960576000004$$

$$a_7=a_1·r^{n-1}=75\cdot {1.08}^{7-1}=75\cdot {1.08}^6=75\cdot 1.5868743229440005=119.01557422080005$$

$$a_8=a_1·r^{n-1}=75\cdot {1.08}^{8-1}=75\cdot {1.08}^7=75\cdot 1.7138242687795209=128.53682015846405$$

$$a_9=a_1·r^{n-1}=75\cdot {1.08}^{9-1}=75\cdot {1.08}^8=75\cdot 1.8509302102818825=138.8197657711412$$

$$a_{10}=a_1·r^{n-1}=75\cdot {1.08}^{10-1}=75\cdot {1.08}^9=75\cdot 1.9990046271044333=149.9253470328325$$