Question

quantos termos possui a P.A.(-5,2,...,65)? Tenho grandes dúvidas e peço que expliquem a questão!

Answer 1

$PA(-5,2,...,65)\\\\ a_1=-5\\ a_n=65\\ r=2-(-5)\to 2+5\to 7\\ n=?\\\\\\ a_n=a_1 +(n-1).r\\\\\\ 65=-5+(n-1).7\to\\\\ 65=-5+7n-7\to\\\\ 65+5+7=7n\to \\\\ 77=7n\to \\\\n= \dfrac{77}{7} \to \\\\ \boxed{\boxed{n=11}}\\\\ \\\\PA(-5, 2, 9, 16, 23, 30, 37, 44, 51, 58, 65)$