Question

quantos são os multiplos de 7 compreendidos entre 100 e 748

Answer 1

AE,

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~multiplos~de~7\\(100,101,102,103,104, \overbrace{\dfrac{105}{} , \dfrac{112}{},..~, \dfrac{742}{}},743,744,745,746,747,748)\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|~~~~~~~~~~~~~~~~~|\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1~~~~~~~~~~~~~~~a_n$

Pela fórmula do termo geral da P.A...

$a_n=a_1+(n-1)r\\ 742=105+(n-1)\cdot7\\ 7n-7=742-105\\ 7n-7=637\\ 7n=637+7\\ 7n=644\\\\ n= \dfrac{644}{7}\\\\ \Large\boxed{\text{n}=92~multiplos}$