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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.