Sequence Problem

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me_1234: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Sun Nov 30, 2014 7:21 pmFollowed by: 2 members; Thanked: 1 times

by me_1234 » Tue Dec 09, 2014 2:50 pm

Can someone help explain this problem?

In the arithmetic sequence t1, t2, t3...., tn...t1 = 23 and tn = tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

Answers:

-1

7

10

14

20

Correct answer is 10.

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Source: Beat The GMAT — Problem Solving | Tue Dec 09, 2014 2:50 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Tue Dec 09, 2014 4:35 pm

melanie.espeland wrote:Can someone help explain this problem?

In the arithmetic sequence t1, t2, t3...., tn...t1 = 23 and tn = tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

Answers:

-1

7

10

14

20

Correct answer is 10.

An arithmetic sequence is a simple sequence in which each term is an equal amount different, d, from the previous term.

In the arithmetic sequence 2 4 6 8 10..., each term is just 2 greater than the term before it. 2 would be t1, or alternatively t0, and each of the other terms is t2, t3, t4...

In these cases it can be pretty easy to find the value of a term.

For a term tn, tn = t1 + (n - 1)d. So in the case of 2 4 6 8 10..., the sixth term, t6, is 2 + (6 - 1)2 = 12

One can also work it backwards to find n, which is the question in this case.

Translated the question is basically, How many times do we need to add the difference, -3, to 23 to get to -4?

t1 = 23 and d = -3

So we have -4 = 23 + (n - 1)-3

-27 = (n - 1)-3

9 = n - 1

n = 10

Do you need to memorize the above formula? Not really. If you see a sequence on the test, it is likely that this formula will not fit that sequence anyway.

What you do need is to understand sequence notation and get the general idea of how sequences work so that you can apply that creatively when you see a sequence question on the test.

Last edited by MartyMurray on Tue Dec 09, 2014 5:15 pm, edited 5 times in total.

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by [email protected] » Tue Dec 09, 2014 4:44 pm

Hi melanie.espeland,

Questions that use "sequence notation" are relatively rare on Test Day (you'll probably see just 1), but the math behind the sequence is usually some fairly simple arithmetic (add, subtract, multiply, divide).

Here, we're given the first term in the sequence (23) and we're told that each term thereafter is 3 LESS than the preceding term. Once you understand how the sequence "works", in many cases, it's really easy to just "map out" the sequence. We're asked which term in the sequence equals -4.....

1st = 23
2nd = 20
3rd = 17
4th = 14
5th = 11
6th = 8
7th = 5
8th = 2
9th = -1
10th = -4

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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me_1234: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Sun Nov 30, 2014 7:21 pmFollowed by: 2 members; Thanked: 1 times

by me_1234 » Tue Dec 09, 2014 5:13 pm

Thank you both for feedback. As an fyi, I just took a GMAT official practice exam and there were two sequence problems (this being one of them).

Sincerely,

Melanie

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Dec 09, 2014 5:42 pm

Hi melanie.espeland,

Between the Randomizer and the experimental questions that appear on Test Day, you could see even more than that. Most Test Takers see just one question that uses sequence notation (so that subject won't be a big part of your Test Day experience); if you take a much broader definition of "sequences", then you could lump a number of different question types into that category.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Dec 09, 2014 8:13 pm

Alternate approach:

T(n) = T(n) - 3.

According to the formula above, each term is 3 less than the preceding term.
The result is an EVENLY SPACED SET.

To count the number of integers in an evenly spaced set, use the following formula:
(biggest - smallest)/interval + 1.
The interval is the distance between successive terms.

Here, the interval is 3, since each term is 3 less than the preceding term.
Since the biggest term = 23 and the smallest term = -4, we get:
Number of terms = (biggest - smallest)/interval + 1 = [23 - (-4)]/3 + 1 = 10.

The correct answer is C.

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