If the sequence S has 300 terms, what is the 293rd term of S

SOLUTION

If the sequence S has 300 terms, what is the 293rd term of S?

(1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term. \(S_{293}=S_{298}+5*2=-616+10=-606\). Sufficient.

(2) The first term of S is -22. Clearly insufficient.

Answer: A.
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We are given that sequence S has 300 terms, and we need to determine the 293rd term of S.

Statement One Alone:

The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.

Statement one defines the pattern of the sequence. We are given that each term of S after the first is 2 less than the preceding term. Thus, we know that we can determine the value of the 293rd term.

If we were forced to determine the 293rd term we could determine that value. We know that the 293rd term is 5 terms before the 298th term. Thus, the 298th term is 5(2) = 10 less than the 293rd term, or in other words, the 293rd term is 10 more than -616, the 298th term. So the 293rd term is -606.

Remember, because we are answering a data sufficiency question, we can stop as soon as we know we are able to determine the value of the 293rd term, and so we don't need to perform the math to calculate its actual value.

Statement one is sufficient. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The first term of S is -22.

Since we do not have any information about the pattern defining the sequence, statement two is not sufficient to answer the question.

The answer is A.
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Statement 1 :

we know : Tn=a+(n-1)d where
Tn=value of the nth term
a=first term
n= nth term
d=difference of the each term...

From the first statement we have all the values of the above equation we can find out a. We do not need to calculate. After finding a we know we can find the value of 298th term.

so A is sufficeint....

2) Only the first term is given. we have two unknown values d and n .. so the statement is insufficient

Answer is A.

i) T298= -616 and common difference=-2
from this we can calculate T293, hence sufficient.

ii) T1= -22, nothing else is provided or known, hence insufficient.

Hence A is the answer.

Thanks.

Have you tried easiest way?
The 298th term of S is -616
The 297th term of S is -614
The 296th term of S is -612
The 295th term of S is -610
The 294th term of S is -608
The 293rd term of S is -606
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Easy one ... Answer is A.
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1) if the 298 term of S is -616, and each thereafter is 2 less than the preceding term, you know that term 297, or 298 can also be solved, that's sufficient enough to find the 293rd term.

2) the stem is tricky because the question wants you to carry over and second guess yourself, or make you choose C, so be careful,
for statement 2: you still need a base to start, such as statement 1), 298 term of s is -616, and 2) you're lacking the difference per term, such as statement 1), the difference is -2 per term. So lacking these two makes this statement NOT SUFF.

Common Sense, really. NO MATH!

Kudos is this helps !

I think S(293) will be -608 and not -606

Heres my calculation

S(n)=a-2(n-1)

s(298)=a-2(297)

--> -616=a-594
--> a=-22

S(293) = -22 - 2(293)
= -22-586
= -608

Your right, i was just trying to figure out another way to solve the problem just in case someone might benefit by looking at it in another way.

How stupid of me

made a mistake

S(293) = -22 - 2(293)
= -22-586
= -608

should be

S(293) = -22 -2(293-1)
= -22-584
=-606

If the sequence S has 300 terms, what is the 293rd term of S?

(1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
(2) The first term of S is -22.

Alternate method:
Sequence nth term formula for arithmetic progression is : [a+(n-1)d]

Where a= 1st term, n= no of the term we want to find and d= difference between 2 terms.

here we know that n=293
Now lets take the easy one first: option B : we are given that a= -22 : Clearly not sufficient, we need difference d.

Now Option A.
298th term is 616
so 616 = [a + (298-1)2] => we can find A from this and then can find 293rd term by [a+(293-1)2]
Hence A is sufficient.

If you want to understand this formula here is the link : https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/03 ... gressions/
One more useful formula is also provided here

here statement tells us it is a Ap series with one term given and D given so its sufficient
Statement 2 is not correct for obvious reasons as its no AP
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Is it true that to find a specified value within in a set we need primarily two things: (1) a reference term (S_298 = -616) and (2) a general formula that specifies the number associated with the a specified element of the set?

If the sequence S has 300 terms, what is the 293rd term of S?

(1) The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
(2) The first term of S is -22.

Prompt analysis
There is an arithmetic progression of 300 terms.

Superset
The answer will be real number.

Translation
We know that tn = a +(n-1)d. In order to know that t293, we need the value of a and d.

Statement analysis

St 1: t298 =-616 and d = -2. Therefore t298 =a +297d = a +292d +5d = t293 +5d
Therefore -616 =t293 -10. t293 =-606. ANSWER. Hence option b,c,e eliminated.
St 2: a =-22. Since we have no idea about any other information, it is INSUFFICIENT.

Option A

If we are given any one of the terms and the relationship between two terms, we can find any term in that sequence. The answer is A

Target question: What is the 293rd term of S?

Statement 1: The 298th term of S is -616, and each term of S after the first is 2 less than the preceding term.
So, each term is 2 less than the previous term.
Since term_298 = -616, we can conclude that:
term_297 = -614
term_296 = -612
term_295 = -610
So, we COULD keep going to determine the value of term_293 (which happens to be -606)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The first term of S is -22.
Since this statement tells us nothing about the NATURE of the sequence, there's no way to determine the value of term_293
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

Tn= a + (n-1)d
1. a=-2 given t298=-616 put these values in the above mentioned equation a can be found. Sufficient
2. a=-22 not sufficient
A

The other method to solve this question would be if we see how series is formed.
a2= a1-2
a3= a2-2= a1-4
a4=a3-2=a1-6
an=a1-2(n-1)

So we can calculate a1 and hence calculate the required value .
So Option A Sufficient

Knowing the first term will not help until we know how the series is formed. Hence Option B is insufficient.
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