Consider the sequence a1 = 3; a2 = 5; a3 = 9; a4 = 17; a5 = 33; : : :
(a) Determine a (fi rst-order) recurrence relation for this sequence, and use it to fi nd a6.
(b) Find a closed formula for an for all n 1, and use induction on your recurrence from (a) to prove that
it's correct. (Hint: think about powers of 2.)
The recurrence relation is to multiply the previous number by 2, then subtract 1.
So a6=65
The closed formula then is 2n-1
Plugging the numbers in the sequence into that equation will prove the equation correct
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