Question

what are the next two terms 1,1,5,17,61,217​

Answer 1

To solve these you need to find a pattern that satisfies all numbers you already have. One that works here is:

the 3rd term is the sum of twice the first term and 3 times the second

the 4th term is the sum of twice the 2nd and 3 times the 3rd

the 5th  term is the sum of twice the 3rd and 3 times the 4th

the 6th  term is the sum of twice the 4th and 3 times the 5th

so the 7th should be  the sum of twice the 5th and 3 times the 6th

or 61*2+217*3= 773

You should now be able check that the next one is 2753

Answer 2

657,1681

are your answers