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GMAT Exam  >  GMAT Questions  >  Sequence S is defined as Sn = X + (1/X), wher... Start Learning for Free
Sequence S is defined as Sn = X + (1/X), where X = Sn – 1 + 1, for all n > 1.
If S1= 201, then which of the following must be true of Q, the sum of the first 50 terms of S?
  • a)
    13,000 < Q < 14,000
  • b)
    12,000 < Q < 13,000
  • c)
    11,000 < Q < 12,000
  • d)
    10,000 < Q < 11,000
  • e)
    9,000 < Q < 10,000
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Sequence S is defined as Sn = X + (1/X), where X = Sn – 1 + 1, f...
To find each successive term in S, we add 1 to the previous term and add this to the reciprocal of the previous term plus 1.
S1= 201



The question asks to estimate (Q), the sum of the first 50 terms of S. If we look at the endpoints of the intervals in the answer choices, we see have quite a bit of leeway as far as our estimation is concerned. In fact, we can simply ignore the fractional portion of each term. Let’s use S2 ≈ 202, S3 ≈ 203. In this way, the sum of the first 50 terms of S will be approximately equal to the sum of the fifty consecutive integers 201, 202 … 250. 
To find the sum of the 50 consecutive integers, we can multiply the mean of the integers by the number of integers since average = sum / (number of terms). 
The mean of these 50 integers = (201 + 250) / 2 = 225.5
Therefore, the sum of these 50 integers = 50 x 225.5 = 11,275, which falls between 11,000 and 12,000. The correct answer is C.
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Most Upvoted Answer
Sequence S is defined as Sn = X + (1/X), where X = Sn – 1 + 1, f...
In this sequence, each term Sn is defined as the reciprocal of the previous term X. The value of X is equal to the previous term Sn.

Let's start with the first term, S1. Since there is no previous term, we can assign any value to it. Let's say S1 = 1.

Now, we can calculate the value of S2 using the formula Sn = X (1/X), where X = Sn.

S2 = X (1/X)
S2 = S1 (1/S1)
S2 = 1 (1/1)
S2 = 1

Similarly, we can calculate the value of S3 using the same formula, but with X = S2.

S3 = X (1/X)
S3 = S2 (1/S2)
S3 = 1 (1/1)
S3 = 1

Continuing this pattern, we can see that all the terms in the sequence will be equal to 1. So, the sequence S is a constant sequence with all terms equal to 1.
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Sequence S is defined as Sn = X + (1/X), where X = Sn – 1 + 1, for all n > 1.If S1= 201, then which of the following must be true of Q, the sum of the first 50 terms of S?a)13,000 < Q < 14,000b)12,000 < Q < 13,000c)11,000 < Q < 12,000d)10,000 < Q < 11,000e)9,000 < Q < 10,000Correct answer is option 'C'. Can you explain this answer?
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