Which of the following numbers will replace the question mark (?) in the given series?
1, 3, 10, 41, ?, 1237

The correct option is 206.

To find the missing number in the series, let us analyze the pattern of progression between consecutive terms:

1st term = 1

To get the 2nd term, multiply the 1st term by 2 and add 1:
$(1\times 2)+1=3$

To get the 3rd term, multiply the 2nd term by 3 and add 1:
$(3\times 3)+1=10$

To get the 4th term, multiply the 3rd term by 4 and add 1:
$(10\times 4)+1=41$

Following this established pattern, we multiply the n-th term by $(n+1)$ and add 1 to obtain the next term.

Thus, to get the 5th term (?), we multiply the 4th term (41) by 5 and add 1:
$(41\times 5)+1=205+1=206$

We can verify this pattern with the 6th term in the series by multiplying the 5th term (206) by 6 and adding 1:
$(206\times 6)+1=1236+1=1237$

Since the verification matches the last term, the missing number is 206.