Question

quantos termos existem na PA (1/2;2;7/2;...;50)?

Answer 1

$dados:\begin{cases}a _{1}= \frac{1}{2}\\ r=a _{2}-a _{1}~\to~r=2- \frac{1}{2}~\to~r= \frac{3}{2}\\ a _{n}=50\\ n=? \end{cases}$

Usando a fórmula do termo geral da P.A., temos:

$a _{n}=a _{1}+(n-1)r\\\\ 50= \frac{1}{2}+(n-1) \frac{3}{2}\\\\ 50= \frac{1}{2}+ \frac{3}{2}n- \frac{3}{2}\\\\ \frac{100}{\not2}= \frac{3}{\not2}n- \frac{2}{\not2}\\\\ 3n=100+2\\ 3n=102\\\\ n= \frac{102}{3}\\\\ \boxed{n=34~termos}$


Espero ter ajudado e tenha ótimos estudos mano (y)