Question

numa pa o 8º termo é 52 e o a9 + a10 = 125. qual o valor da soma dos termos dessa progressão?

Answer 1

$a_8=52\\ a_9=a_8+r\\ \boxed{a_9=52+r}\\\\ a_{10}=a_8+2r\\ \boxed{a_{10}=52+2r}\\\\ a_9+a_{10}=125\\ 52+r+52+2r=125\\ 3r=125-52-52\\ 3r=21\\ r=\frac{21}{3}\\ \boxed{r=7}\\\\ a_8=a_1+7r\\ a_1+7r=52\\ a_1+7.7=52\\ a_1+49=52\\ a_1=52-49\\ a_1=3\\\\ a_{10}=a_8+2r=52+2.7=52+14=66\\\\ S_n=\frac{(a_1+a_n).n}{2}\\\\ S_{10}=\frac{(3+66)10}{2}\\\\ S_{10}=\frac{69.10}{2}\\\\ S_{10}=69.5=345$