If the first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms, then the common ratio is

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Detailed Solution

Let the G.P. be 1 r,r2,r3,..Given, tn=2tn+1+tn+2+tn+3+… to ∞ or tn=2⋅tn+11−r, (∵ common ratio =r)∴ =tn+1tn; or 1−r2=r or 1−r=2r;∴r=13

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