Question

 Dada a PG (x; 3x; .....; 729x), qual o número de termos ?

Answer 1

$<var>PG = (x, 3x, ... , 729x)</var>$

 

$<var>\cdot \ a_{n} = 729x</var>$ 

 

$\cdot \ <var>a_{1} = x</var>$

 

$\cdot \ <var>q = 3</var>$ , pois  $<var>3x : x = 3</var>$

 

$<var>\blacktriangleright a_{n} = a_{1} \cdot q^{n-1}</var>$ define o termo geral da P.G.:

 

$<var>729x = x \cdot 3^{n-1}</var>$

 

$<var>\frac{729x}{x} = 3^{n-1}</var>$

 

$<var>729 = 3^{n-1}</var>$

 

$<var>3^6 = 3^{n-1}</var>$

 

$<var>6 = n - 1</var>$

 

$<var> n = 7</var>$

 

Existem 7 termos nesta P.G.