Question

Determine a quantidade de termos de cada P.A abaixo.
a) (7,11,...,67)
b) (33,30,...,-13)​

Answer 1

Resposta:

a) 16

b) 16

Explicação passo-a-passo:

a) $(7,11,\dots,67)$

$a_{n}=a_1+(n-1)\cdot r$

$a_{n}=67~~~a_1=7~~~r=11-7=4$

$67=7+(n-1)\cdot4$

$67-7=4n-4$

$60=4n-4$

$4n=64$

$n=\dfrac{64}{4}$

$n=16$

b) $(33,30,\dots,-12)$

$a_{n}=a_1+(n-1)\cdot r$

$a_{n}=-12~~~a_1=33~~~r=30-33=-3$

$-12=33+(n-1)\cdot(-3)$

$0=33+12-3n+3$

$3n=48$

$n=\dfrac{48}{3}$

$n=16$