Question

the next number in the series 13,25,51,101,203 ?is

Answer 1

We can see that in the sequence 13,25,51,101,203 ,...

The second number is twice the first number - 1.

The third number is twice the second number + 1.

The fourth number is twice the third number - 1.

and so on ......

So the general term is

$T_{n+1}=2T_{n}+(-1)^{n}, T_1=13,n=1,2,3,...$.

Thus the 6th number is $2*203-1=405$.

Thus the required number is 405.