解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=23$$ 和公比：$$r=2.4347826086956523$$ 插入几何级数的公式：

$$a_1=23$$

$$a_2=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{2-1}=23\cdot {2.4347826086956523}^1=23\cdot 2.4347826086956523=56$$

$$a_3=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{3-1}=23\cdot {2.4347826086956523}^2=23\cdot 5.928166351606806=136.34782608695653$$

$$a_4=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{4-1}=23\cdot {2.4347826086956523}^3=23\cdot 14.433796334347006=331.97731568998114$$

$$a_5=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{5-1}=23\cdot {2.4347826086956523}^4=23\cdot 35.14315629232315=808.2925947234324$$

$$a_6=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{6-1}=23\cdot {2.4347826086956523}^5=23\cdot 85.56594575522159=1968.0167523700966$$

$$a_7=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{7-1}=23\cdot {2.4347826086956523}^6=23\cdot 208.3344766214091=4791.692962292409$$

$$a_8=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{8-1}=23\cdot {2.4347826086956523}^7=23\cdot 507.24916046951785=11666.730690798911$$

$$a_9=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{9-1}=23\cdot {2.4347826086956523}^8=23\cdot 1235.0414341866522=28405.952986293$$

$$a_{10}=a_1·r^{n-1}=23\cdot {2.4347826086956523}^{10-1}=23\cdot {2.4347826086956523}^9=23\cdot 3007.0574049761967=69162.32031445252$$