Question

Numa P.A sabe-se que a1+a5=15 e a3+a6=36. Determine a soma dos 30 primeiros termos dessa P.A​

Answer 1

$a_{5}=a_{1}+4r\\a_{3}=a_{1}+2r\\a_{6}=a_{1}+5r$

$a_{1}+a_{5}=2a_{1}+4r\\a_{3}+a_{6}=2a_{1}+7r$

$-\underline{\begin{cases}2a_{1}+4r=15\\2a_{1}+7r=36\end{cases}}$

$-3r=-21\div(-3)\\r=7$

$2a_{1}+4.7=15\\a_{1}=\dfrac{15-28}{2}=-6,5$

$a_{30}=a_{1}+29r\\a_{30}=-6,5+29.7=196,5$

$s_{30}=\dfrac{30(-6,5+196,5)}{2}\\a_{30}=15.190$

$\boxed{\boxed{\mathsf{s_{30}=2850}}}$