Question

Numa P.A. crescente, a2+ a6 = 20 e a4 + a9= 35. Determine o 1° termo e a razão dessa progressão

Answer 1

Fácil:

$a_2=a_1+r\\\\a_6=a_1+5r\\\\\boxed{a_2+a_6=2.a_1+6r=20} \ \ \ (I)\\\\a_4=a_1+3r\\\\a_9=a_1+8r\\\\\boxed{a_4+a_9=2.a_1+11r=35} \ \ \ (II)\\\\Fazendo \ (II)-(I): \ \ 5r=15 \ \Rightarrow \boxed{\boxed{r=3}}\\\\\\\\\\Substituindo \ r \ em \ (I):\\\\2.a_1+6r=20\\\\2a_1+18=20\\\\2a_1=2\\\\\boxed{\boxed{a_1=1}}$