In the arithmetic sequence t(1), t(2), t(3)....t(n). : PS Archive
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# In the arithmetic sequence t(1), t(2), t(3)....t(n).

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Manager
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In the arithmetic sequence t(1), t(2), t(3)....t(n).  [#permalink]

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25 Mar 2007, 07:42
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In the arithmetic sequence t(1), t(2), t(3)....t(n).
t(1)=23 and t(n)-t(n-1)-3 for each n>1.

What is n if t(n) = -4?

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

View the values in the parenthesis as subscripts.

Director
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25 Mar 2007, 07:56

before explanation just a small amendment in ur question. instead of t(n)-t(n-1)-3, it should be t(n)-t(n-1) = -3

now it makes sense as it will take the shape of arithmatic progression.

please remember in arithmatic progression sequence difference between every consequitive number is fixed, and we call it D. in this case that fixed difference is -3 as given.

suppose A is the first number in the sequence, which is 23 in this case as given t(1) = 23.

Now nth term in the sequence will be A + (n-1)D,

we have t(n) = -4 = A+(n-1)D, putting the values from above we will get n = 10.

regards,

Amardeep
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25 Mar 2007, 08:34

good link for this kind of problem
SVP
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25 Mar 2007, 08:36
(C) as well

I suggest to quickly buit the answer : 23 and -4 are not so far by removing 3.

#1# : 23
#2# : 20
#3# : 17
#4# : 14
#5# : 11
#6# : 8
#7# : 5
#8# : 2
#9# : -1
#10# : -4

It takes u the time to right the number and then to count them (20s?).
Manager
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25 Mar 2007, 09:19
Thanks for the quick reply. OA = 10.

I haven't thoroughly read and understood the explanations yet, but it seems a little complex.

This question was one of the first questions I got from GMATPREP.

Is this normal to get a question of this difficulty (at least it was hard for me) as the very first question?
Director
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25 Mar 2007, 11:12
t(n) - t(n-1) = -3
t(1) = 23
t(2) = 20
t(3) = 17
...
t(n) = 23 - ([n-1] x 3) [started from n=2 since the foruma is true for n>1 and thus the expression (n-1)]
-4 = 23 - 3n + 3 --> n = 10

About the GMATPrep. I think this question is in the 600 to 650 range [middle to upper middle in the difficulty bin].
25 Mar 2007, 11:12
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