Problem Solving

BTGmoderatorLU wrote:Source: Economist GMAT

In a sequence of 12 numbers, each term, except for the first one, is \(12^{11}\) less than the previous term. If the greatest term in the sequence is \(12^{12}\), what is the smallest term in the sequence?

A. \(-12^{11}\)
B. \(0\)
C. \(12^{11}\)
D. \(11\cdot12^{11}\)
E. \(12^{12}\)

The OA is C

Since each subsequent term is less than the previous term, the greatest term in the sequence would be the first term = \(12^{12}\).

Thus,

"¢ II term = I term - \(12^{11}\) = \(12^{12}\) - \(12^{11}\);
"¢ III term = \(12^{12}\) - 2*\(12^{11}\);
"¢ II term = \(12^{12}\) - 3*\(12^{11}\);
.
.
.
"¢ XII term = \(12^{12}\) - 11*\(12^{11}\) = Smallest term

Smallest term = \(12^{12}\) - 11*\(12^{11}\) = 12*\(12^{11}\) - 11*\(12^{11}\) = \(12^{11}\)*[12 - 11] = \(12^{11}\)

The correct answer: C

Hope this helps!

-Jay
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