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

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If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 20 Aug 2012, 02:23
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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.

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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 20 Aug 2012, 02:23
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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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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 21 Aug 2012, 08:51
Bunuel wrote:
RESERVED FOR A SOLUTION.

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.

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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 23 Aug 2012, 20:32
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
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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 23 Aug 2012, 23:09
Easy one ... Answer is A.
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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 24 Aug 2012, 06:11
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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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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 02 May 2013, 19:34
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 ! :)
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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 12 Sep 2014, 13:19
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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 05 Oct 2014, 10:14
Bunuel wrote:
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.


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
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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 05 Oct 2014, 10:23
Expert's post
havoc7860 wrote:
Bunuel wrote:
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.


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


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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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 05 Oct 2014, 10:53
Bunuel wrote:
havoc7860 wrote:
Bunuel wrote:
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.


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


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


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
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Re: If the sequence S has 300 terms, what is the 293rd term of S [#permalink] New post 05 Oct 2014, 22:17
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 : http://www.veritasprep.com/blog/2012/03 ... gressions/
One more useful formula is also provided here
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Re: If the sequence S has 300 terms, what is the 293rd term of S   [#permalink] 05 Oct 2014, 22:17
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