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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

If a sequence is defined using the recurrence relation:

what is the exponent of the term s5 if:

Write the successive terms:

Of course, if we are more advanced we can see that, with each step to the next term the exponent is multiplied by the rank of the term:

This last formula, is something we should be able to 'see' just by examining the recurrence formula.

Since we know (presumably by heart, see the lesson on general skills) that:

we should be able to select the correct answer without any paper and pen.

The analytic formula for the general term can be predicted to be:

and a proof by induction should follow.