A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio. 

Let the G.P. be T₁, T₂, T₃, T₄, …, T₂ₙ.

Number of terms = 2n

According to the given condition,

T₁ + T₂ + T₃ + … + T₂ₙ = 5[T₁ + T₃ + … + T₂ₙ₋₁]

⇒ T₁ + T₂ + T₃ + … + T₂ₙ − 5[T₁ + T₃ + … + T₂ₙ₋₁] = 0

⇒ T₂ + T₄ + … + T₂ₙ = 4[T₁ + T₃ + … + T₂ₙ₋₁]

Let the G.P. be a, ar, ar², ar³, …

∴ (ar(rⁿ − 1)) / (r − 1) = (4 × a(rⁿ − 1)) / (r − 1)

⇒ ar = 4a

⇒ r = 4

Thus, the common ratio of the G.P. is 4.