Question

o número de termos da PG (x⁵³, x⁵⁰, x⁴⁷,..., x‐¹ ) , sendo x um número real positivo e diferente de 1, será?

a) 17
b) 18
c) 16
d) 19​

Answer 1

$q=\dfrac{x^{50}}{x^{53}}=x^{50-53}=x^{-3}\\\\a_n=a_1\cdot q^{n-1}\\\\x^{-1}=x^{53}\cdot(x^{-3})^{n-1}\\\\x^{-1-53}=x^{-3n+3}\\\\-54=-3n+3\\\\-3n=-57\\\\n=19$