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 Post subject: GMAT Sequences
PostPosted: Mon Apr 29, 2013 12:18 pm 
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8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 10th and the 20th terms?

A. 324
B. 335
C. 346
D. 357
E. 368

(A) First, we need to derive a formula so that we do not need to write out the first 20 terms.
The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 10th term is 10 × 11 – 3 = 107.
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 324. The correct answer is choice (A).
----------
Can you please tell me how you came up with the formula: 8 = (11 – 3). 8 + 11 = 19, 19 + 11 = 30, etc.


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 Post subject: Re: GMAT Sequences
PostPosted: Mon Apr 29, 2013 12:19 pm 
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If a sequence is given and you're asked to find the sequence, you should look for the "simple" sequences first, like arithmetic or geometric progressions.

8, 19, 30, 41, 52, ….

19 – 8 = 11
30 – 19 = 11
41 – 30 = 11
52 – 41 = 11

In this sequence we can see right away that the difference between any two consecutive numbers is 11. Therefore it is an arithmetic progression.

The first term is 8, the second one is 8 + 11, the third one is (8 + 11) + 11, etc.

So the formula for finding the n-th term is 8 + 11(n – 1), which is the same as 11n – 3, if we simplify.


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 Post subject: Re: GMAT Sequences
PostPosted: Mon Apr 29, 2013 12:21 pm 
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Does the sequence always start at one as opposed to 0? I used Sn = 11n + 8 and got the trap answer of 346. Please advise.


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 Post subject: Re: GMAT Sequences
PostPosted: Mon Apr 29, 2013 12:21 pm 
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Student wrote:
Does the sequence always start at one as opposed to 0?
A sequence starts with the first element.
If you think of the first element as of the zero one, then you must shift all other elements accordingly. So if a question asks you to calculate the sum of the 10th and the 20th terms, then in your notation it will be the sum of the 9th and 19th terms.

Student wrote:
I used Sn = 11n + 8 and got the trap answer of 346. Please advise.

If you notate the first element as S0 (S0 = 8), then the 10th one will be S9 and the 20th one will be S19.


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 Post subject: Re: GMAT Sequences
PostPosted: Mon Apr 29, 2013 12:22 pm 
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Hello all,
it could be also true that the above sequence is a linear sequence with the d = 11 (a1 = 8, a2 = 8 + 11 = 19, a3 = 19 + 11 = 30 etc.)

Therefore the 10th and the 20th values can be calculated according to the formula an = a1 + (n + 1) × d.

Applying this the result is 368 (E).
Please assist kindly.
Best regards.


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 Post subject: Re: GMAT Sequences
PostPosted: Mon Apr 29, 2013 12:23 pm 
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Quote:
Therefore the 10th and the 20th values can be calculated according to the formula an = a1 + (n + 1) × d.
The formula is NOT correct. You may check this fact by calculating a2 or a3, etc.:
a2 = 8 + (2 + 1) × 11 = 41, which is NOT true.

The proper formula would be An = A1 + (n – 1) × d.


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