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Sequence Problem

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Sequence Problem

by akshatgupta87 » Wed Apr 13, 2011 12:33 pm
Q.) In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is 3.

(2) The second-to-last term is 3^10.


I have one doubt in the 2nd statement.
Since, the second last term is known to us, we can calculate in reverse order and find the fourth term, as for the sequence to be valid it cannot take negative values.
Isn't this possible?
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by maihuna » Wed Apr 13, 2011 1:18 pm
well they cant be negative but they can be less than 1, so 1/3 as first term will differ in fourth than 1 or 3 as start term.

so several first terms are still possible, 3^-x, 3^0, 3^x where x can be any integer.
akshatgupta87 wrote:Q.) we can calculate in reverse order and find the fourth term, as for the sequence to be valid it cannot take negative values.
Isn't this possible?
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by Ian Stewart » Wed Apr 13, 2011 2:41 pm
akshatgupta87 wrote:Q.) In a sequence of terms in which each term is three times the previous term, what is the fourth term?

(1) The first term is 3.

(2) The second-to-last term is 3^10.


I have one doubt in the 2nd statement.
Since, the second last term is known to us, we can calculate in reverse order and find the fourth term, as for the sequence to be valid it cannot take negative values.
Isn't this possible?
I don't like the casual language of the question (it is not true that the first term is 3 times the previous term, since there is no term before the first), and the 'trick' in statement 2 isn't likely to show up on the test.

Still, you might know that the second-last term is 3^10, but without any information about how many terms you have, you can't tell what the 4th term is. Your sequence might be

3^7, 3^8, 3^9, 3^10, 3^11

and the fourth term might be equal to 3^10, or it might be

3^4, 3^5, 3^6, 3^7, 3^8, 3^9, 3^10, 3^11

for example, in which case the fourth term is 3^7, among many other possibilities.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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