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If sequence S has 100 terms, what is the 83rd term of S?

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If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 02 Jun 2016, 11:52
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If sequence S has 100 terms, what is the 83rd term of S?

(1) The first term of S is 23
(2) Each term after the first term of S is 5 less than the preceding term

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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 02 Jun 2016, 13:49
Stm1 : a = first term = 23. We don't know anything about the kind of the series. So not sufficient,
Stm2 : Now we know that we are dealing with an arithmetic progression. nth term of an AP = a + (n-1)d.
We know n = 83, and we know d = -5, But we don't know a, the first term of the series. Not sufficient.

Combining, we know all we need to calculate the 83rd term. Hence C.
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If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post Updated on: 03 Jun 2016, 00:49
st1: a=23, n=100, we dont have information about d=? so it is not sufficient.
st2: n=100, d=5, we dont have information about a=? so it is also not sufficient.
st1 & st2:
a=23, n=100, d=5. we can find 83 rd term by using the formula.
t83= a+(83-1)d.
so c is the answer.

Originally posted by Harish Yannam on 03 Jun 2016, 00:23.
Last edited by Harish Yannam on 03 Jun 2016, 00:49, edited 1 time in total.
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 03 Jun 2016, 00:37
Bunuel wrote:
If sequence S has 100 terms, what is the 83rd term of S?

(1) The first term of S is 23
(2) Each term after the first term of S is 5 less than the preceding term


Statement 1

We only know the first term and total terms. But we do not know the Common difference as well as the type of progression. (AP or GP)
Not sufficient.


Statement 2

This statement tells us that common difference is (-5).
However we do not know the first term.
So we cannot find the 83rd term with this information.

Not sufficient.

Combining Statements 1 and 2

We know a = 23. We know d = -5
Nth term = a+(n-1)d

So sufficient.

(C) is the answer.
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 03 Jun 2016, 11:32
Bunuel wrote:
If sequence S has 100 terms, what is the 83rd term of S?

(1) The first term of S is 23
(2) Each term after the first term of S is 5 less than the preceding term


(1) The first term of S is 23
No idea if the sequence is consecutive numbers or random numbers or any other pattern. Not sufficient

(2) Each term after the first term of S is 5 less than the preceding term.
We are not given any term. Not sufficient.

Combining both statements:-

If first term is 23 and each following term is 5 less than the previous term, then we could find out 83rd term. Sufficient

C is the answer
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 05 Jun 2016, 05:02
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Bunuel wrote:
If sequence S has 100 terms, what is the 83rd term of S?

(1) The first term of S is 23
(2) Each term after the first term of S is 5 less than the preceding term



The question didn't mention any progression between the number of element.Only progression/relationship between numbers can guarantee a specific sequence. For example, In an arithmetic progression, 83 th term=A + D(83-1) ,A=First number of the sequence,D=common difference between two numbers.

Statement 1: Knowing only first term(A=23) is not sufficient to know the 83th term.Still we need more information.Not Sufficient

Statement 2: knowing only the common difference between two numbers (D=5)in not sufficient to know any specific progression.Not Sufficient

Combining two statements together we can find the 83 th term =23+5(83-1)=23+410=433,Sufficient

So, Correct Answer C
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 15 Jun 2016, 15:25
Top Contributor
Bunuel wrote:
If sequence S has 100 terms, what is the 83rd term of S?

(1) The first term of S is 23
(2) Each term after the first term of S is 5 less than the preceding term


Target question: What is the 83rd term of S?

Statement 1: The first term of S is 23
We have no idea how this sequence progresses. So, there's no way to determine the 83rd term.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Each term after the first term of S is 5 less than the preceding term
Okay, so we know HOW the sequence progresses, but we don't know the specific value of any term.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Term 1 = 23 (from statement 1)
Term 2 = 23 - 5 = 18 (from statement 2)
Term 3 = 18 - 5 = 13
And so on....
Since we COULD keep this pattern going indefinitely, we COULD easily find the value of the 83rd term.

Of course, we're not going to waste any time determining the actual value of the 83rd term. All we need to do is determine whether the combined statements are sufficient to answer the target question.

Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer =

Cheers,
Brent
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 23 Sep 2016, 21:32
Is it true that C is the correct answer because to determine a specific value in the list, we need (1) a starting/reference point and (2) a formula that is applied to generate all of the elements of the set?
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 23 Feb 2017, 05:48
Prompt analysis
An arithmetic progression following the sequence as tn = a +(n-1)d has 100 terms.

Superset
The answer will be any real number.

Translation
In order to find t83, we need a and d or any two equation to solve for a and d.

Statement analysis

St 1: a = 23. We don't have any idea about d. INSUFFICIENT. Hence a and d eliminated.
St 2: d = -5. We don't have any idea about a. INSUFFICIENT. Hence a, b and d eliminated.
St 1 & St 2: we know a =23, n=83 and d =-5. We can find the value of t83 with the above mentioned formula

Option C
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 20 Aug 2017, 11:54
Hi,
I have a doubt in this question.
Some people are saying common difference is 5 and and some are saying saying common difference is -5
I know Sn = a1+(n-1)d but, shuld I take d as +ve or -ve?
If we take from question it is clear that d is -ve..

Can some one help me .

Thanks,
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Re: If sequence S has 100 terms, what is the 83rd term of S?  [#permalink]

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New post 03 Oct 2017, 08:27
Hi Brent,

Could you please explain - how could we find value of 83rd term by recognizing the pattern for this?
Re: If sequence S has 100 terms, what is the 83rd term of S? &nbs [#permalink] 03 Oct 2017, 08:27
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