Investigate!
Each day your supply of magic chocolate-covered espresso beans doubles (each one splits in half), but then you eat 5 of them. You have 10 at the start of day 0.
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Write out the first few terms of the sequence. Then give a recursive definition for the sequence, and explain how you know it is correct.
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Prove, using induction, that the last digit of the number of beans you have on the
th day is always a 5 for all -
Find a closed formula for the
th term of the sequence, and prove it is correct by induction.