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Sequence S is defined as Sn=Sn-1 + 1 +1/(Sn-1 + 1) for all n [#permalink]
19 Dec 2012, 06:18

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Difficulty:

35% (medium)

Question Stats:

57% (03:05) correct
43% (01:25) wrong based on 76 sessions

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S?

Re: Sequence S is defined as for all n > 121. [#permalink]
19 Dec 2012, 07:49

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daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S_1 = 100

S_2 = \frac{101^2 + 1}{101} \approx 101 (Since 1 is negligible when compared to 101^2)

So, the series is almost an arithmetic progression with a=100, d=1,

We have got to find the sum of "n" terms where "n" is 16.

S_{16} = \frac{16}{2}*(2*100 + (16-1)*1)

= 8*215 = 1720

Answer is C.
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Re: Sequence S is defined as for all n > 121. [#permalink]
19 Dec 2012, 20:14

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Expert's post

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 has been given a big value i.e. 100 instead of the usual 0/1 etc. Why? Because 1/100 is negligible when added to 101

Re: Sequence S is defined as for all n > 121. [#permalink]
19 Dec 2012, 21:07

VeritasPrepKarishma wrote:

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 has been given a big value i.e. 100 instead of the usual 0/1 etc. Why? Because 1/100 is negligible when added to 101

The sum will be a little more than 1720. Answer (c)

i would say the question is wrong or, atleast, not an exact GMAT type question...why to assume N as an integer...it is not specified in the question that n is an integer....n could be 1.2, 1.2,....etc for n>1 when n is not an integer.... i am thinking in the GMAT prospective...what is the source of this qtn?

Last edited by muralilawson on 19 Dec 2012, 21:53, edited 2 times in total.

Re: Sequence S is defined as for all n > 121. [#permalink]
19 Dec 2012, 21:19

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 = 100

S2 = 100 + (1 + \frac{1}{101}) If you will notice 1 + \frac{1}{101} is approximately 1... S2 = 100 + 1 is approx. ~ 101

S3 = 101 + (1 + \frac{1}{101}) If you wil notice 1 + \frac{1}{101} is approximately 1... S3 = 101 + 1 approx. ~ 102

Re: Sequence S is defined as for all n > 121. [#permalink]
19 Dec 2012, 21:52

muralilawson wrote:

VeritasPrepKarishma wrote:

daviesj wrote:

Sequence S is defined as Sn = (Sn-1 +1) + {1 / (Sn-1 +1)} for all n > 1. If S1 = 100, then which of the following must be true of Q, the sum of the first 16 terms of S? (A) 1,600 ≤ Q ≤ 1,650 (B) 1,650 ≤ Q ≤ 1,700 (C) 1,700 ≤ Q ≤ 1,750 (D) 1,750 ≤ Q ≤ 1,800 (E) 1,800 ≤ Q ≤ 1,850

method to solve plz...

S1 has been given a big value i.e. 100 instead of the usual 0/1 etc. Why? Because 1/100 is negligible when added to 101

The sum will be a little more than 1720. Answer (c)

i would say the question is wrong or, atleast, not an exact GMAT question...why to assume N as an integer...it is not specified in the question that n is an integer....n could be 1.2, 1.2,....etc for n>1 when n is not an integer.... i am thinking in the GMAT prospective...

Since this is a PS question and not a DS question, we are free to make that assumption. "n" is only a subscript indicating the ordinal number of each term and hence can be taken to be integers.
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