Question

solve the puzzle 2,5,17,65,257,__

Answer 1

HEY FRND..

THE SEQUENCE IS..

1) 2 = 1^2 + 1
2) 5 = 2^2 + 1
3) 17 = 4^2 + 1
4) 65 = 8^2 + 1
5) 257 = 16^2 + 1

now the next number would be 32.

so 32^2 + 1 = 1025


ANSWER IS 1025

Answer 2

Concept:

Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players.

Given:

We are given the puzzle:

2,5,17,65,257,__

Find:

We need to solve the puzzle.

Solution:

First let us identify the pattern.

Here, in this puzzle, we can see that first, a number is being squared and then, 1 is added to the result.

Also, the every next number being squared is the multiple of 2.

2=1²+1

5=2²+1

17=4²+1

64=8²+1

257=16²+1

So, from this pattern, we get that the next number will be:

32²+1=1025

64²+1=4097

Therefore, after solving the puzzle, we get the complete puzzle as 2, 5, 17, 65, 257, 1025, 4097.

#SPJ3