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a₅= ???
a₁₁= 8
a₁₂= 16
Regla general de una PG.
an=a₁ r ⁿ⁻¹
Sustituimos los valores conocidos.
8=a₁ r ¹¹⁻¹
8/r¹° =a₁
16=a₁ r ¹³⁻¹
16/r¹² = a₁
Igualando: a₁ = a₁ ...
8/r¹° = 16/r¹²
r¹² / r¹° = 16/8
r² = 2
r= √2
Para obtener a₅ es necesario conocer a₁.
a₁= 8/r¹°
a₁= 8/(√2)¹°
a₁= 8/2⁵
a₁= 8/32
a₁= ¼
Ahora, podemos obtener: a₅
an= a₁ r ⁿ⁻¹
a₅= ¼ (√2)⁵⁻¹
a₅= ¼ (√2)⁴
a₅= ¼ (2²)
a₅= ¼ (4)
a₅= 1 --> R/.