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Arithematic Progression

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by coolhabhi » Thu Oct 10, 2013 3:06 am
The sum of first four terms of an Arithematic Progression is 28 and sum of the first eight terms of the same series is 88. Find the sum of the first 16 terms of the series

A)346
B)340
C)304
D)268

OA : C

I got the answer but I am looking for a shortcut. If anyone has it then please post it..
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by GMATGuruNY » Thu Oct 10, 2013 3:25 am
coolhabhi wrote:The sum of first four terms of an Arithematic Progression is 28 and sum of the first eight terms of the same series is 88. Find the sum of the first 16 terms of the series

A)346
B)340
C)304
D)268

OA : C
Sum of the first 4 terms = 28.
Sum of the next 4 terms = sum of the first 8 terms - sum of the first 4 terms = 88-28 = 60.

Difference between the sums = 60-28 = 32.
Implication:
Each set of 4 terms yields a sum that is 32 greater than the sum of the PRECEDING 4 terms.
Thus:
Sum of the next 4 terms = 60+32 = 92.
Sum of the last 4 terms = 92+32 = 124.

Final tally:
28 + 60 + 92 + 124.
Since the sum of the units digits = 8+0+2+4 = 14, the correct answer choice must have a units digit of 4.

The correct answer is C.
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by coolhabhi » Thu Oct 10, 2013 3:35 am
Ain't that a solution.. Thanks Mitch.. Your the best..
GMATGuruNY wrote:
coolhabhi wrote:The sum of first four terms of an Arithematic Progression is 28 and sum of the first eight terms of the same series is 88. Find the sum of the first 16 terms of the series

A)346
B)340
C)304
D)268

OA : C
Sum of the first 4 terms = 28.
Sum of the next 4 terms = sum of the first 8 terms - sum of the first 4 terms = 88-28 = 60.

Difference between the sums = 60-28 = 32.
Implication:
Each set of 4 terms yields a sum that is 32 greater than the sum of the PRECEDING 4 terms.
Thus:
Sum of the next 4 terms = 60+32 = 92.
Sum of the last 4 terms = 92+32 = 124.

Final tally:
28 + 60 + 92 + 124.
Since the sum of the units digits = 8+0+2+4 = 14, the correct answer choice must have a units digit of 4.

The correct answer is C.
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by Brent@GMATPrepNow » Thu Oct 10, 2013 5:56 am
coolhabhi wrote:The sum of first four terms of an Arithematic Progression is 28 and sum of the first eight terms of the same series is 88. Find the sum of the first 16 terms of the series

A)346
B)340
C)304
D)268
I should point out that the GMAT will not assume that students know the definition of an Arithmetic Progression. Instead, they will describe the sequence.

Basically, an arithmetic progression is a sequence in which each term can be calculated by adding some constant, k, to the preceding term.

Some examples:
6, 8, 10, 12, 14,... (adding 2 to each term to get the next term)
-1, 6, 13, 20, 27,... (adding 7 to each term to get the next term)
10, 7, 4, 1, -2, -5,.... (adding -3 to each term to get the next term)

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Brent
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by [email protected] » Thu Oct 10, 2013 11:47 am
Hi coolhabhi,

Brent is correct in that a GMAT question would define the term "arithmetic sequence" before asking you to use one to answer a question. Nothing about this prompt is in the proper GMAT format, so either the source for this "GMAT question" is questionable or you're not actually studying for the GMAT.

If the GMAT is your focus, then you really should be using defined, GMAT-specific practice material and not just "math questions."

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by alexvchang » Sat Oct 12, 2013 9:07 am
GMATGuruNY, I don't understand how the implication (each set of 4 terms yields a sum that is 32 greater than the sum of the PRECEDING 4 terms) follows if the FIRST 4 terms yield a sum that is only 28. What am I not seeing here?

Thanks,
Alex
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