In an infinite G.P. each term of the GP is equal to the sum of all the following terms. Find the ratio of this G.P.
Explanation:
Let the first term be a and the common ratio be r.
Given, each term of the the GP is twice the sum of all the following terms.
Let’s consider the 3rd term of the G.P.
∴ ar2 = ar3 + ar4 + ar5 + … ∞
⇒ ar2 = (ar3)/(1-r)
⇒ 1 – r = r
⇒ r = ½
Hence, option (a).
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