consider the following recursively defined sequence: a1 = 2 an = a(n-1) - 3 for

ID: 3143343 • Letter: C

Question

consider the following recursively defined sequence:

a1 = 2

an = a(n-1) - 3 for n >=2 (n-1 is below a not an exponent)

In this question, we will prove that a n = 3n + 5 for all n>=1. fill in the blanks.

let p(n) = _____________. we prove that for all n is an element of Z, if n >=0, then P(n).

base case: the base case is n = ___________

proof of the base case: __________

induction step:

the induction hypothesis is ____________

our goal in the induction hypothesis step is top rove ________ ________________.

proof of the induction step:

a1=2
given formula is an=a(n-1)-3
plut n=2 to find a2
we get
a2=a(2-1)-3=a(1)-3=2-3=-1...(i)

Now plug n=2 into formula an=3n+5 that you want to prove
a2=3*2+5=6+5=11...(ii)

from (i) and (ii) we can see that a2 has different values which is not possible.
You may have posted wrong equation.

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.