paulovitor000
74

# 1.      (MACK – SP)  Numa PA de 100 termos,  a3 = 10 e a98 = 90. A soma de todos os termos é:

(1) Respostas
Jailson123

$a_3=10$ $a_{98}=90$ $a_n=a_1+(n-1)r$ $a_3=a_1+2r$ $a_{98}=a_1+97r$ $a_1+2r=10~(i)$ $a_1+97r=90~(ii)$ Fazendo $(ii)-(i)$: $(a_1+97r)+(a_1+2r)=90-10$ $95r=80$ $r=\dfrac{80}{95}$ $r=\dfrac{16}{19}$ $a_1+2r=10$ $a_1+\dfrac{32}{19}=10$ $a_1=10-\dfarc{32}{19}$ $a_1=\dfrac{158}{19}$ $a_{100}=\dfrac{158}{19}+99\cdot\dfrac{16}{19}$ $a_{100}=\dfrac{1~742}{19}$ $S_{100}=\dfrac{(\frac{158}{19}+\frac{1~742}{19})100}{2}=\frac{1~900}{19}\cdot50=100\cdot50=5~000$