Discrete mathematics: incursion

[goofyfootsp]

Homework Statement

a 1= 2, a k+1, 2ak-1

Homework Equations

What is the 5th term

The Attempt at a Solution

a1= 2
a2=2(2)-1= 3
a3=2(3)-1=5
a4=2(4)-1=7
a5=2(5)-1=9

5th term =9?

 

[Mark44]

Homework Statement

a 1= 2, a k+1, 2ak-1

Homework Equations

What is the 5th term

The Attempt at a Solution

a1= 2
a2=2(2)-1= 3
a3=2(3)-1=5
a4=2(4)-1=7
a5=2(5)-1=9

5th term =9?

That would be recursion, not incursion, which has a very different meaning.
The recursion formula you provided is wrong, and I guarantee you that it was not the one you were given in the problem.

a 1= 2, a k+1, 2ak-1

From the work you show later on, it appears that you meant this:
a_1 = 2
a_(k+1) = 2*a_(k) -1

So,
a_1 = 2
a_2 = 2*a_1 -1 = 2(2) - 1 = 3
a_3 = 2*a_2 -1 = 2(3) - 1 = 5
So far, so good, but your next terms are wrong. Here's a hint:

a_4 = 2*a_3 - 1 = 2(?) - 1
a_5 = 2*a_4 - 1 = 2(?) - 1

Mark

 

[goofyfootsp]

That equation you presented was correct I did not know how to type it out properly.

I see so

a_4 = 2*a_3 - 1 = 2(?) - 1
a_5 = 2*a_4 - 1 = 2(?) - 1

a_4 = 2*a_3 -1 = 2(5) - 1 = 9

a_5 = 2* a_4-1 = 2(9) -1 = 17

Is that correct?

 

[Mark44]

That equation you presented was correct I did not know how to type it out properly.

I see so

a_4 = 2*a_3 - 1 = 2(?) - 1
a_5 = 2*a_4 - 1 = 2(?) - 1

a_4 = 2*a_3 -1 = 2(5) - 1 = 9

a_5 = 2* a_4-1 = 2(9) -1 = 17

Is that correct?

Yep, it is.

 

[goofyfootsp]

Thanks, for your help Mark!

Syd