Question

Obter a razão de cada p.g
a)(4,8,16,32)

b)(7,21,63)

Answer 1

A razão de uma PG, se dá dividindo um termo pelo anterior. Ou então pode usar a fórmula:

$a_n=a_1*q^{n-1}$


 Vamo lá =)


$a)~~(4,8,16,32) \\\\ a_1=4~;~n=4~;~a_n=32\\\\ \\a_n=a_1*q^{n-1} \to~~ 32=4*q^{4-1}\to~~ 32=4*q^3\to~~ \dfrac{32}{4}=q^3\to\\ \\ 8=q^3 \to~~ 2^{\not3}=q^{\not3}\to~~ \large\boxed{q=2}\\\\\\ Ou~~simplesmente:\\\\ \dfrac{a_2}{a_1}\to~~ \dfrac{8}{4} \to~~ \boxed{q=2}$





$b)~~(7,21,63) \\\\ a_1=7~;~n=3~;~a_n=63\\\\ \\a_n=a_1*q^{n-1} \to~~ 63=7*q^{3-1}\to~~ 63=7*q^2\to~~ \dfrac{63}{7}=q^2\to\\ \\ 9=q^2 \to~~ 3^{\not2}=q^{\not2}\to~~ \large\boxed{q=3}\\\\\\ Ou~~simplesmente:\\\\ \dfrac{a_3}{a_2}\to~~ \dfrac{63}{21} \to~~ \boxed{q=3}$