Question

calcule o 7º termo de uma PA em que a soma dos 10 primeiros termos é -170 e r = -2

Answer 1

$\mathrm{PA=(a_1,\dots,a_{10},\dots,a_n)\ \ \|\ \ S_{10}=-170\ \ \|\ \ r=-2}\\\\ \mathrm{S_{10}=-170\ \to\ \dfrac{(a_1+a_{10}).10}{2}=-170\ \to\ }\\\\ \mathrm{\to\ a_1+a_{10}=\dfrac{-170}{5}\ \to\ a_1+a_1+9r=-34}\\\\ \mathrm{2a_1+9(-2)=34\ \to\ 2a_1=52\ \to\ \boxed{\mathrm{a_1=26}}}\\\\ \mathrm{a_n=a_1+(n-1)r\ \to\ a_7=a_1+6r}\\\\ \mathrm{a_7=26+6(-2)\ \to\ a_7=26-12}\\\\ \boxed{\boxed{\mathbf{a_7=14}}}$