Dúvida básica - P.A

por Gabriel Rodrigues Qui 26 Set 2013, 17:28

Na P.A, em que a_p = x e a_q = y, com p diferente de q, calcular o termo a_(p+q).

Resp.: xp + yq / p-q

por JuniorE Qui 26 Set 2013, 18:12

Tem certeza do gabarito ou do enunciado?

$Dúvida básica - P.A Gif.latex?%5C%5Ca_p%3Da_1+%28p-1%29.r%5C%5Ca_q%3Da_1+%28q-1%29.r%5C%5C%5C%5Cx-y%3D%28p-1%29r+%281-q%29r%5C%5C%5C%5Cr%3D%5Cfrac%7Bx-y%7D%7Bp-q%7D%5C%5C%5C%5Ca_1%3Dy-%28q-1%29.%5Cfrac%7Bx-y%7D%7Bp-q%7D%5C%5C%5C%5Ca_1%3D%5Cfrac%7B%28p-q%29y-%28q-1%29%28x-y%29%7D%7Bp-q%7D%5C%5C%5C%5Ca_%7Bp+q%7D%3Da_1+%28p+q-1%29.r%5C%5C%5C%5Ca_%7Bp+q%7D%3D%5Cfrac%7B%28p-q%29y-%28q-1%29%28x-y%29%7D%7Bp-q%7D+%28p+q-1%29.%5Cfrac%7Bx-y%7D%7Bp-q%7D%5C%5C%5C%5Ca_%7Bp+q%7D%3D%5Cfrac%7B%28p-q%29y-%28q-1%29%28x-y%29+%28p+q-1%29$

Se você usar por exemplo a PA (3,4,5,6,7,8,9) com a_p=4 (p=2) e a_q=5 (q=3), colocando na fórmula:

a_(p+q)=(4.2-5.3)/(2-3)
7=7

abraço!