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Re: The nth term of an increasing sequence S is given by Sn = Sn1 + Sn2 [#permalink]
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01 Jun 2017, 23:13
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Let the first 5 terms of sequence S be represented as: S1, S2, S3, S4, S5 Here S3 = S2+S1, S4 = S3+S2, S5 = S4+S3 ..
Let the first 5 terms of sequence S' be represented as: S1', S2', S3', S4', S5' Here S4' = S3'S2', S5' = S4'S3'
Now lets look at the statements: (What I will try to do is write as many terms as possible in terms of either S2 or S2' because our objective is to calculate mean of S2 & S2', which we will get once we have the sum S2+S2')
Statement 1. S4S2 = 14, Or S4 = 14+S2, But S4 = S3+S2.. this means S3 = 14 Thus S5 = S4+S3 = 14+S2 + 14 = 28+S2 So S5 can be written in terms of S2 as '28+S2'.
We are given that S5 = S5', so S5' = 28+S2 Now, S5' = S4'  S3' and S4' = (S3'S2')  S3' = S2'
See, S5' can be written as (28+S2) and it can also be written as 'S2' . Equating them both: 28+S2 = S2' Or S2+S2' = 28 We have their sum, so their average = 28/2. Sufficient.
Statement 2. S4' + S2' = 14. Now, S4' = S3'S2' or S4'+S2' = S3'
But S4' + S2' = 14, So S3'=14.... Thus we can say S4' = S3'S2' = 14S2', and S5' will become: S5' = S4'S3' = 14S2'  14 = S2'
We are given that S5 = S5' so S5 = S2' or S4+S3 = S2' Replacing S4 with S3+S2, we have S3+S2 + S3 = S2' or S2+S2' = 2S3
We have their sum in terms of variable S3, so mean cannot be calculated. Insufficient.
Hence A answer
