If sequences S has 240 terms, what is the 239th term of S?

Hi Bunuel and all,

I know OA says E, I don't think I'm wrong either unless my understanding is...

thus consider/ please correct my understanding for this sentence. Because it seems to me that with arithmetic progression -consecutive progression and the term made known, then only can the answer be found.

My answer was C, because we know that is an arithmetic progression and the first and 239th term is 952. Therefore 1st, 2nd,....239th term => 952/238 = 4. Therefore 1st to 240th term is 1st term + the arithmetic progression difference = 4 + 956 = 960.

GKA

(2) says that the difference between 239th term and the first term is 952. This is true for ANY evenly spaced set with the common difference of 4.

To get this right:

(1) Statement 1 says: \(A_N = A_{N-1}-4\). The question asks for \(A_{239}=?\). So all we needed to solve was one of the real values values such as \(A_{50}\) or any other?

Can you confirm this Bunuel?

_________
Yes, that's right.

Need your help in correcting my understanding.

1. Each term of S after the first term is 4 less than the preceding term
2. The 239th term of S is 952 less than the first term

If first term = a, second term = a-4, so common difference = -4 (from 1).
tn = a + (n-1)d so we can write: a-952 = a + (239-1)d
1+2
a-952 = a + (239-1) (-4),we will find a and then we can find 239th term. Please help me understand where exactly I am unable to interpret the statements correctly.

Hi Gauraku- I had a similar idea at first but I believe you're overcomplicating. One of the key ideas I always try to keep in mind is: how is the GMAT trying to trick me? What does it want me to believe? In this case, the GMAT wants you to think exactly as you have. However, when you simplify your equation, a = 0. While this could be a value of the first term, the first term could also equal 1000 and the 239th term equal 8 OR the first term could equal 10000 and 239th term equal 9,048. All three of these pairs follow the rule of being 4 less than the preceding term.

The main idea is that when we divide 952 by 4, we get 238, meaning that the 238th term is -4*238 less than the 1st- this does not give any new information since we already know all terms are spaced 4 apart from statement 1.

IMPORTANT: Statement 2 can be directly inferred from statement 1.
That is, if each term is 4 less than the previous term (e.g., 19, 15, 11, etc) then we can conclude that term2 will be 4 less than term1.
We can also conclude that term3 will be 8 less than term1, and:
term4 will be 12 less than term1.
term5 will be 16 less than term1.
.
.
.
term239 will be 952 less than term1 (same as statement 2).

So, as you can see, statement 2 DOES NOT PROVIDE ANY EXTRA INFORMATION beyond the information that statement 1 provided.

So, if statement 1 is NOT SUFFICIENT (which is clearly the case), then statement 2 cannot be NOT SUFFICIENT.
More importantly, the statements combined are NOT SUFFICIENT.

Answer:
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If sequences S has 240 terms, what is the 239th term of S?

1) Each term of S after the first term is 4 less than the preceding term
2) The 239th term of S is 952 less than the first term

When solving such type of questions always think what is required to get the value of 239 Term

If we know how the series is formed, or if we are given the certain relationship between terms, or are the terms of the seq repetitive or is some kind of pattern in these terms.

So stmt 1 : Gives us how the seq is formed.

It says ( Xn)= (Xn-1) -4. This means the seq is an AP.

So 239 term will be X239= (Xn-1)+ (239-1) (-4)
so we are given X 239= X(n-1)-952.
So we need to find the value of Xn-1 to get the value of X239

Stmt 2: This is what has been derived from STMT 1

So We cannot find the value if required term till we have at least value of Xn-1 or any other term of the seq.

Hi Bunuel,

The common difference would be -4 in this Question, right?

_______________________________
Yes.

Thanks a lot for your quick reply!!

Just because the question stem mentions sequence, can we assume that it is an AP?

If not, then statement 1 gives us 2 information, Sequence is AP and difference=-4
whereas statement 2 just gives me that 239th term is 952 less than the first, it does not tell me that it is an A.P.

Can I apply this logic to all the problems then. Is there an issue with my logic?

chetan2u
gmatbusters

Hi nitesh50

please find response to your queries:

Just because the question stem mentions sequence, can we assume that it is an AP?
- NO, it can be any sequence. (a particular order in which related things follow each other. it can be AP, GP and any other sequence)


If not, then statement 1 gives us 2 information, Sequence is AP and difference=-4
Right

whereas statement 2 just gives me that 239th term is 952 less than the first, it does not tell me that it is an A.P.
Right


Can I apply this logic to all the problems then. Is there an issue with my logic?
YES, applying this logic , we get that it is an AP with common difference of (-4), and hence 239th term is obviously 238*4 = 952 less than first.
Statement 2 gives no extra info.
Now since first term , a, is unknown 239th term can not be determined.

Answer E

im the slowest ???? took me 54 seconds

If sequences S has 240 terms, what is the 239th term of S?
In order to find the 239th term, we need:
1. the value of one of the terms in sequence S
2. the common change between sequential terms.

1) Each term of S after the first term is 4 less than the preceding term
This gives us the common change (difference = -4), but we don't know the value of any terms. Not sufficient.

2) The 239th term of S is 952 less than the first term
This tells us is that \(a_1 - 952 = a_{239}\)
So we have the range between the 1st and 239th, but not the change between or the value of either term. Not sufficient.

3) We still only know the common change but don't have an actual value for any terms in the sequence.

\(a_{1} - 952 = a_{239}\) or that \(a_{239} = a_1 + -4*(239-1)\)

\(a_1 - 952 = a_1 + -4*(238)\)

\(- 952 = -4*(238)\)

\(0 = 0\)

Not sufficient to find \(a_{239}\).

n = 240

We need to answer the question:

a₂₃₉ = ?

Statement One Alone:

=> Each term of S after the first term is 4 less than the preceding term.

Although we know that S is an arithmetic sequence with a common difference of d = -4, we don’t know the value of any of its terms.

Statement one is not sufficient. Eliminate answer choices A and D.

(Note: If we knew the value of any term of the sequence, then, using the common difference, we could move back or forward to reach the 239th term.)

Statement Two Alone:

=> The 239th term of S is 952 less than the first term.

a₂₃₉ = a₁ - 952

Clearly, different values of a₁ would give us different values of a₂₃₉.

Statement two is not sufficient. Eliminate answer choice B.

Statements One and Two Together:

We still don’t know the value of any term of S.

The two statements together are not sufficient.

Answer: E

(Note: Statement two follows from statement one. From statement one, we know the S is an arithmetic sequence. So, we have:

a₂₃₉ = a₁ + (n – 1)d

a₂₃₉ = a₁ + (239 – 1)(-4)

a₂₃₉ = a₁ - 952, which is the same information that statement two gives us.)

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