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Sn represent the sum of n terms of a certain sequence, where each term
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27 Mar 2023, 08:35
27 Mar 2023, 08:35
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Question Stats:
25% (01:29) correct
74% (01:14) wrong based on 43 sessions
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\(S_n\) represent the sum of n terms of a certain sequence, where each term after the first term of the sequence is obtained by adding a constant c, where c > 0, in the preceding term
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE SEQUENCES
Quantity A |
Quantity B |
\(S_{n+1}\) |
\(S_{n+2}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE SEQUENCES
Re: Sn represent the sum of n terms of a certain sequence, where each term
[#permalink]
27 Mar 2023, 18:34
27 Mar 2023, 18:34
1
Constant C can be both positive and negative and Zero.
Note : 1 1 1 1 1 ...... is also an increasing sequence
If C > 0 S n+2 > S n + 1
If C < 0 S n+2 < S n + 1
If C = 0 S n+2 = S n + 1
Cannot be Determined
Note : 1 1 1 1 1 ...... is also an increasing sequence
If C > 0 S n+2 > S n + 1
If C < 0 S n+2 < S n + 1
If C = 0 S n+2 = S n + 1
Cannot be Determined
Re: Sn represent the sum of n terms of a certain sequence, where each term
[#permalink]
22 Apr 2023, 16:29
22 Apr 2023, 16:29
1
Expert Reply
Given 𝑆𝑁 represents the sum of 𝑁 terms of a certain sequence. It is said that the sequence is obtained by adding a positive constant C to the previous term, which means it is in Arithmetic Progression.
As we know, Arithmetic Progression is a sequence obtained by adding or subtracting a constant from the previous terms. This leads to a common difference between each of the two consecutive terms.
If 𝐴 be the first term and 𝐷 be the common difference then the sequence proceed as follows:
1st, 2nd, 3rd, …………………………………., 𝑁th term
𝐴, 𝐴 + 𝐷, 𝐴 + 2𝐷, 𝐴 + 3𝐷, … … … , 𝐴 + (𝑁 − 1)𝐷
Where 𝑁 is the last term.
Let 𝐴 be the first term. The common difference here is 𝐷.
So, 𝑆𝑛 can be expressed as:
𝑆𝑁 = [𝐴] + [𝐴 + 𝐷] + [𝐴 + 2𝐷] + ⋯ + [𝐴 + (𝑁 − 1)𝐷] = Sum of 𝑁 terms
Accordingly, 𝑆𝑁+1 can be expressed as:
𝑆𝑁+1 = 𝑆𝑢𝑚 𝑜𝑓 (𝑁 + 1) 𝑇𝑒𝑟𝑚s
Similarly, 𝑆𝑁+2 can be expressed as:
𝑆𝑁+2 = 𝑆𝑁+1 + extra term
So in both quantities everything boils down to the extra term, considering also that Sn+1 is common to both and this means we have 0
QA is 0
QB the extra term.
However, we do not know the extra term if it is positive, negative, or zero
D is the answer
As we know, Arithmetic Progression is a sequence obtained by adding or subtracting a constant from the previous terms. This leads to a common difference between each of the two consecutive terms.
If 𝐴 be the first term and 𝐷 be the common difference then the sequence proceed as follows:
1st, 2nd, 3rd, …………………………………., 𝑁th term
𝐴, 𝐴 + 𝐷, 𝐴 + 2𝐷, 𝐴 + 3𝐷, … … … , 𝐴 + (𝑁 − 1)𝐷
Where 𝑁 is the last term.
Let 𝐴 be the first term. The common difference here is 𝐷.
So, 𝑆𝑛 can be expressed as:
𝑆𝑁 = [𝐴] + [𝐴 + 𝐷] + [𝐴 + 2𝐷] + ⋯ + [𝐴 + (𝑁 − 1)𝐷] = Sum of 𝑁 terms
Accordingly, 𝑆𝑁+1 can be expressed as:
𝑆𝑁+1 = 𝑆𝑢𝑚 𝑜𝑓 (𝑁 + 1) 𝑇𝑒𝑟𝑚s
Similarly, 𝑆𝑁+2 can be expressed as:
𝑆𝑁+2 = 𝑆𝑁+1 + extra term
So in both quantities everything boils down to the extra term, considering also that Sn+1 is common to both and this means we have 0
QA is 0
QB the extra term.
However, we do not know the extra term if it is positive, negative, or zero
D is the answer
