. 2, 5, 17, 65, _______, 1025

The pattern is: previous term x 4 + 1. 2x4+1=9, but we have 5. Let me reconsider: 2 to 5 is +3, 5 to 17 is +12, 17 to 65 is +48. The additions are 3, 12, 48 - each time multiplying by 4. Next addition: 48x4=192. 65+192=257. Check: 257x4+1=1029, but we need 1025. Actually the pattern is: multiply by 4 and add 1. 2x4+1=9 (doesn't match 5). Alternative: 4^n+1: 4⁰+1=2, 4¹+1=5, 4²+1=17, 4³+1=65, 4⁴+1=257, 4⁵+1=1025.