Question

calcule a soma dos 15 primeiros termos PA (-3,4,11...95)

Answer 1

$PA(-3,4,11,...,95)\\\\a_{1}=-3\\a_{2}=4\\\\r=a_{2}-a_{1}\\r=4-(-3)\\r=4+3\\r=7\\\\a_{n}=95\\n=?\\\\a_{n}=a_{1}+(n-1)\cdot{r}\\95=-3+(n-1)\cdot(7)\\95=-3+7n-7\\95=7n-10\\7n=105\\n=15\\\\\\S_{n}= \dfrac{(a_{1}+a_{n})\cdot{n}}{2}\\\\\\S_{n}= \dfrac{(-3+95)\cdot15}{2}\\\\\\S_{n}= \dfrac{92\cdot15}{2}\\\\\\S_{n}= 690$