Question

Quantos termos tem a PG (2,6,18) para que a soma de seus termos resulte em 177146?

Answer 1

q = a2/a1
q = 6/2
q = 3

$Sn = a1.\frac{q^{n}-1}{q-1}$

Sendo assim,

$177146 = 2.\frac{3^{n}-1}{3-1}\\\\\\ 177146=2.\frac{3^{n}-1}{2}\\\\\\ \frac{2.177146}{2}=3^{n}-1\\\\\\ 177146+1=3^n\\\\\\ 177147 = 3^n \\\\\\ 3^{11}=3^n\\\\\\11 = n$

Há 11 termos.