Question

What are the next two terms in the pattern 3, 6, 5, 10,9, 18, 17, . . .?

Answer 1

They could be `34`, `33`

Explanation:

This sequence seems to come from an alternating iterative rule where on odd steps you double the previous number and on even steps you subtract `1` from the previous number.

The formula for a general term of the sequence may be written:

`a_n = { (2^((n+1)/2)+1, "if n is odd"), (2^(n/2+1)+2, "if n is even") :}`

To avoid the condition on `n` being odd or even, you can use `(-1)^n` to formulate it as follows:

`a_n = (2^((n+1)/2)+1) * (1-(-1)^n)/2 + (2^(n/2+1)+2) * (1+(-1)^n)/2`

Answer 2

It's actually easier than that, unless you need a formula.

Explanation:

The pattern is: double, then subtract 1, or

multiply by 2, subtract 1.

`3*2=6` and `6-1=5`

`5*2=10` and `10-1=9`

`9*2=18` and `18-1=17`

The continuation would be:

`17*2=34` and `34-1=33`

`33*2=66` and `66-1=65`

and so on.