OFFICIAL EXPLANATIONHi All,
We're told that all of the terms in a sequence are positive and the 3rd term of sequence A is 15. We're asked for the 2nd term of the sequence.
1) The 1st term of A is 5.
Knowing 2 terms of the sequence is not enough to define how the sequence 'works' - or any of the other terms in the sequence. It's certainly possible that the sequence is Arithmetic and 'increases by 5' from term to term... meaning that the first three terms would be 5, 10 and 15.... and the answer to the question would be 10.
However, it's also possible that the sequence is Geometric and each term increases by some constant product (such as √3)... meaning that the first three terms would be 5, 5√3 and 15... and the answer to the question would be 5√3.
Fact 1 is INSUFFICIENT
2) Each term of A after the 1st term is y times the preceding term.
Fact 2 tells us how the sequence works, but without the first term in the sequence, we cannot determine the second term in the sequence.
Fact 2 is INSUFFICIENT
Combined, we know...
-The 1st term of A is 5.
-Each term of A after the 1st term is y times the preceding term.
With the information in both Facts, we know that the first term is 5, the third term is 15 and each term increases by some constant product. The only way for that sequence to exist is if y = √3... meaning that the first three terms are 5, 5√3 and 15... and the answer to the question is 5√3.
Combined, SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Hi, from both, Y^2 =3==> Y= +/- √3, shouldn't the answer still be E?? or should I ignore the -ve sign because its an AP.?