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

Question

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

FacelessMan · Answer

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.

Harish Yannam · Answer

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.

adiagr · Answer

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.

Divyadisha · Answer

(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

AbdurRakib · Answer

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

BrentGMATPrepNow · Answer

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 =  C

Cheers,
Brent

GMAT2645 · Answer

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?

KrishnakumarKA1 · Answer

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

sasidharrs · Answer

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,

santro789 · Answer

Hi Brent,

Could you please explain - how could we find value of 83rd term by recognizing the pattern for this?

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

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GMAT Data Sufficiency (DS) Questions

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

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