In the arithmetic sequence

[agha79]

GMAT prep exam one question. I was unable to find this in the forms. I searched using first few words of the question as a search.

I have always struggled with sequence problems. I have a lot of trouble finding the pattern and same was the case in this one. I think even taking the initial step for this one was very difficult for me. Please help me understand the below problem and any tips on approaching such problems more efficiently.

NOTE: MGMAT form readers please note in below question "t1, t2,..." is not multiplying numerical values with ts. i.e value of "t1" has number "1" as a subscript of "t". Also tn-1 has "n-1" as a subscript of "t." On the form I was unable to post subscripts so wanted to make sure question is clear to everyone. )

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

a) -1
b) 7
c) 10
d) 14
e) 20

OA: C

[tim]

okay, you've copied down the question incorrectly, but i think i can derive what it was meant to say. the tn-1 part should say tn = tn-1 - 3, which means each subsequent term is 3 less than the previous term. if t1 = 23 and tn = -4, that means we have dropped 27. if each new term is 3 less than the previous term, that means we have moved 9 terms from the starting point (9 jumps of -3 gives the drop of 27). 9 terms from t1 will be t10..

[agha79]

Thanks Tim - Great explanation and just understanding what "tn = tn-1 - 3" means was easy enough for me to get the answer without reading your full explanation. Is this question really this straight forward? I really feel bad now that I got such a simple question wrong.

[jnelson0612]

Hi agha, I think your error in transcribing the problem caused your difficulties. Glad it makes sense now!

[terryfshs]

You are not alone, I had difficulties when I read this question.

My problem stemmed from not knowing how to break down the sentence. I read the sequence as:

"t1, t2, t3,........tn..., t1 = 23"

I thought, sequence starts at t1, goes to tn, and back to t1, and the entire sequence is equal to 23?

I then had a "Deer meets headlight" moment.

[RonPurewal]

Thanks Tim - Great explanation and just understanding what "tn = tn-1 - 3" means was easy enough for me to get the answer without reading your full explanation. Is this question really this straight forward? I really feel bad now that I got such a simple question wrong.

sequence notation creates artificial difficulty for most people taking this test, because most test takers don't understand it very well. therefore, yes, if a problem is written in sequence notation, then the likelihood that it's actually quite simple (once you decode all the notation, of course) is surprisingly high.