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Consider the sequence a1 = 3; a2 = 5; a3 = 9; a4 = 17; a5 = 33; : : : (a) Determ

Mathematics
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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.)

Apr 18th, 2015

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

Apr 18th, 2015

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Apr 18th, 2015
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