given the recursive sequence defined below, find the first four terms.
a1=3
an=2an-1-n
a1 = 3
a2 = 2(a1)-2 = 6-2 = 4
a3 = 2(a2)-3 = 8-3 = 5
a4 = 2(a3)-4 = 10-4 = 6
Extra inductive proof to support the pattern shown above
By induction, if an= n+2, then
a(n+1)= 2(n+2)-(n+1)
=n+3
which follows the inductive assumption.
With the base case of a1 and a2, this hence proves that an=n+2.
a1 = 3
a2 = 2(a1)-2 = 6-2 = 4
a3 = 2(a2)-3 = 8-3 = 5
a4 = 2(a3)-4 = 10-4 = 6
Extra inductive proof to support the pattern shown above
By induction, if an= n+2, then
a(n+1)= 2(n+2)-(n+1)
=n+3
which follows the inductive assumption.
With the base case of a1 and a2, this hence proves that an=n+2.