A G.P. consists of an even number of terms. If the sum of all the terms is 6 times the sum of terms occupying odd places, then find its common ratio.

Question

Philoid · Accepted Answer

Let the terms of G.P. be T₁, T₂, T₃, T₄, … T_2n.

Number of terms = 2n

According to question,

T₁ + T₂ + T₃ + … + T_2n = 6 [T₁ + T₃ + … + T_2n–1]

⇒ T₁ + T₂ + T₃ + … + T_2n – 6 [T₁ + T₃ + … + T_2n–1] = 0

⇒ T₂ + T₄ + … + T_2n = 4 [T₁ + T₃ + … + T_2n–1]

Let the G.P. be a, ar, ar², ar³, …

⇒ ar = 4a

∴ r = 4

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