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

If a sequence is defined using the recurrence relation:

equation

what is the exponent of the term s5 if:

equation

Write the successive terms:

equation

equation

equation

equation

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:

equation

equation

equation

equation

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:

equation

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:

equation

and a proof by induction should follow.